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Newly added pages can be seen from this page. Keep visiting to this page so that you will remain updated.en-usMathMon, 19 Nov 2018 18:54:13 -0500Mon, 19 Nov 2018 18:54:13 -0500math-only-math.comNov 19, Independent Variables and Dependent Variables | Variable | Formula
https://www.math-only-math.com/independent-and-dependent-variables.html1eafd8904181fd09c8157fe35055420aIf x stands for any of the real numbers from the set R then x is a variable over R. For example, if x is the over number in an one-day international cricket match of 50 overs then x is a variable over the set {1, 2, 3, 4, ...., 48, 49, 50}. Suppose, x is the side of a squareMon, 19 Nov 2018 18:54:11 -0500Nov 19, Class Interval | Overlapping and Nonoverlapping Class Intervals
https://www.math-only-math.com/class-interval.html7b3aa349616306b08ce7f9dd58bc22dfIn order to express raw data in the form of grouped data we use classes (or class intervals) for the values of the variables. Depending upon the method of grouping data, class intervals can be divided into two categories. (i) Overlapping Class Intervals: If the values of aMon, 19 Nov 2018 16:15:28 -0500Nov 15, Tally Marks | Tally Mark Represents Frequency | Use of Tally Marks
https://www.math-only-math.com/tally-marks.htmlc54c6975b5d143e2b129d44437fa08adWe will discuss here how to use Tally marks. To count the number of times a value of the variable appears in a collection of data, we use tally mark ( / ). Thus tally mark represents frequency. Observe the tally marks and the corresponding frequencies:Thu, 15 Nov 2018 17:12:12 -0500Nov 14, Class Boundaries |How to Find Class Boundaries? |Statistics Dictionary
https://www.math-only-math.com/class-boundaries.html07d72e9cc41e11ef244037fcb2a1f9eeHere we will learn class boundaries or actual class limits For overlapping class intervals, the class limits are also called class boundaries or actual class limits. In the case of nonoverlapping class intervals, the class limits are different from class boundaries.Wed, 14 Nov 2018 14:58:17 -0500Nov 13, Cumulative Frequency | Frequency Distribution | Class Interval
https://www.math-only-math.com/cumulative-frequency.html040a6cc72bfc971ccc00f033a4323ddeHere we will learn cumulative frequency. The cumulative frequency of a value of a variable is the number of values in the collection of data less than or equal to the value of the variable. For example: Let the raw data be 2, 10, 18, 25, 15, 16, 15, 3, 27, 17, 15, 16.Tue, 13 Nov 2018 17:41:34 -0500Nov 13, Constructing Frequency Distribution Tables | Classified / Unclassified
https://www.math-only-math.com/constructing-frequency-distribution-tables.html75576b035f355458417ba6a168605df8Here we will learn how to construct frequency distribution tables. Following is a collection of raw data showing the ages (in years) of 30 students of class. 14, 15, 14, 16, 15, 13, 17, 16, 17, 16, 17, 12, 13, 12, 14, 15, 16, 15, 18, 12, 17, 17, 18, 13, 14, 13, 16, 15Tue, 13 Nov 2018 17:11:29 -0500Nov 3, Nonoverlapping Class Intervals into Overlapping Class Intervals
https://www.math-only-math.com/nonoverlapping-class-intervals-into-overlapping-class-intervals.htmlbb0d12cf4b8b063c7f4302d329785a60We will learn here how to convert nonoverlapping class intervals into overlapping class intervals. Conversion of Nonoverlapping Class intervals into Overlapping Class intervals: If the nonoverlapping class intervals are a - b, c - d, e - f, etc., the gaps between theSat, 3 Nov 2018 18:21:35 -0400Nov 1, Class Mark | Class Mark Statistics | What is Class Mark?
https://www.math-only-math.com/class-mark.html7888cdc10ed3bc69250fcc2a3061423eHere we will learn class mark. The class mark of a class interval = (Actual lower limit + Actual upper limit)/2 = (Sum of Class Boundaries)/2. For Example: The class mark of the overlapping class interval 10 – 20 = (10 + 20)/2 = 15.Thu, 1 Nov 2018 18:11:35 -0400Nov 1, Class Size Statistics | What is Class Size? | Statistical Data
https://www.math-only-math.com/class-size.html20a391612208951db80feeb98b1c45dcHere we will learn class size. The class size of an overlapping or nonoverlapping class interval = actual upper limit – actual lower limit = difference of class boundaries. For example: The class size of the overlapping interval 10 - 20 = Actual upper limit – actual lowerThu, 1 Nov 2018 15:56:03 -0400Oct 28, Class Limits |What is the Class Limit in Statistics?|Find Class Limits
https://www.math-only-math.com/class-limits.htmlfeca8b1b790454b4f47c7ce41b78a784We will discuss here about the class limits. Let the class intervals for some grouped data 5 – 15, 15 – 30, 30 – 45, 45 – 60, etc. Here, all the class intervals are overlapping and the distribution is continuous. 5 & 15 are called the class limits of the class intervalSun, 28 Oct 2018 16:53:27 -0400Oct 25, Frequency Distribution | Unclassified Frequency Distribution
https://www.math-only-math.com/frequency-distribution-a.html9c509b5c9a3941b1a9bde75ae1254aeeIn the above Table 1 we have an example of unclassified frequency distribution. It shows the number of students obtaining certain marks. For example, the table shows 4 marks were attained by 3 students, 20 marks were obtained by 7 students, etc. So the frequency of 4 marksThu, 25 Oct 2018 18:53:32 -0400Oct 12, Worksheet on Median of Ungrouped Data | Find the Median of Collection
https://www.math-only-math.com/worksheet-on-median-of-ungrouped-data.htmlffed5a5a2c42bcb3f401156a3366f954Practice the questions given in the worksheet on median of ungrouped data. 1. Find the median of the following. (i) The first seven even natural numbers (ii) 5, 0, 2, 4, 3 (iii) 25, 22, 28, 23, 21, 27, 25, 24, 20 2. Find the median of the following. The first six odd naturalFri, 12 Oct 2018 16:48:18 -0400Oct 12, Worksheet on Mean of Ungrouped Data | Find the Mean Weight/Expenditure
https://www.math-only-math.com/worksheet-on-mean-of-ungrouped-data.html7d0a20b36bebf021113d852dc84044b5Practice the questions given in the worksheet on mean of ungrouped data. 1. Find the mean of the following. (i) The first five positive integers. (ii) The first six even natural numbers. 2. Find the mean of the following data. (i) 7, 9, 3, 5, 8, 6 (ii) 4, 11, 0, 5, 10Fri, 12 Oct 2018 15:26:46 -0400Sep 29, Problems on Median of Ungrouped Data|Ungrouped Data to Find the Median
https://www.math-only-math.com/problems-on-median-of-ungrouped-data.html1f6dabb992155c98cae2c8954693f2c4Here we will learn how to solve the different types of problems on median of ungrouped data. 1. The heights (in cm) of 11 players of a team are as follows: 160, 158, 158, 159, 160, 160, 162, 165, 166, 167, 170. The number of variates = 11, which is odd. Therefore, median =Sat, 29 Sep 2018 16:19:12 -0400Sep 28, Problems on Mean of Ungrouped Data | Ungrouped Data to Find the Mean
https://www.math-only-math.com/problems-on-mean-of-ungrouped-data.html44cfd4bd0d2563ce3c8905f37474f293Here we will learn how to solve the different types of problems on mean of ungrouped data. 1. (i) Find the mean of 6, 10, 0, 7, 9. (ii) Find the mean of the first four odd natural numbers. Solution: (i) We know that the mean of five variates Fri, 28 Sep 2018 16:28:57 -0400Sep 25, Median of Raw Data |The Median of a Set of Data|How to Calculate Mean?
https://www.math-only-math.com/median-of-raw-data.html91eca1a97d8b2c9bd0f6dd101791aa61The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts. Method of finding median Take the following steps to find the median of raw data. Step I: Arrange the raw data in ascendingTue, 25 Sep 2018 20:10:55 -0400Sep 25, Mean of Ungrouped Data | Mean Of Raw Data | Mean of Arrayed Data
https://www.math-only-math.com/mean-of-ungrouped-data.htmlcb025bd8d7f0ae6db885204d9e5eb195The mean of data indicate how the data are distributed around the central part of the distribution. That is why the arithmetic numbers are also known as measures of central tendencies. Mean Of Raw Data: The mean (or arithmetic mean) of n observations (variates)Tue, 25 Sep 2018 19:05:20 -0400Sep 22, Frequency of the Statistical Data|Frequency of Set of Statistical Data
https://www.math-only-math.com/frequency-of-the-statistical-data.html7850dfc3087a3346c0829cc6e9368e67The frequency of a value of a variable is the number of times it appears in a collection of data. Example: What is the frequency of 12 in the following data? Solution: 12 appears thrice in the collection. So, the frequency of 12 is 3. Solved Example: The weights (in kg) ofSat, 22 Sep 2018 18:36:41 -0400Sep 20, Range of the Statistical Data | Range of a Set of Statistical Data
https://www.math-only-math.com/range-of-the-statistical-data.html7894037b8351af4e975265798a088c5aThe difference between the greatest and the least values of a variable in a collection of data is called the range of the data. For Example: In collection A, the greatest value of marks obtained is 90 while the least value of the same is 4. So, the range of the data = 90 - 4Thu, 20 Sep 2018 18:41:11 -0400Sep 20, Statistical Variable |Variables in Statistics|Variables and Statistics
https://www.math-only-math.com/statistical-variable.html854467b75d5f8b711ff6f4309dc4ad76The quantity whose different values during observation constitute the collection of data is called a statistical variable. In collection A, the marks obtained by the students is a variable. If we denote the marks obtained by x then x is a variable in the collection.Thu, 20 Sep 2018 16:49:26 -0400Sep 19, Representation of Data | Raw Data | Arrayed Data | Grouped Data
https://www.math-only-math.com/representation-of-data.html9348f731bbbe61baa40832d5be44b20eCollection A (shown below) represents the marks obtained by 50 students in a test of 100 marks. In the collection above, 80, 70, etc., are called the terms of the collection. Depending on the form of expression, data may be raw (i.e., ungrouped) or arrayed. I. Raw Data:Wed, 19 Sep 2018 18:51:39 -0400Sep 17, Statistics and Statistical Data | Sample or Representative Data
https://www.math-only-math.com/statistics-and-statistical-data.htmlbc3a19648709cb82356a8254ae9ad61cStatics is that branch of mathematic which deals with the collection, classification, representation, analysis and interpretation on numerical data. The study of statistics started nearly 2000 years ago. Today statistics holds an important place in the fields of economicsMon, 17 Sep 2018 15:51:08 -0400Sep 16, Problems on Cumulative-Frequency Curve | Problems on Ogive Graph
https://www.math-only-math.com/problems-on-cumulative-frequency-curve.html2179603055af55690f9e177de1678238We will discuss here some of the problems on frequency polygon. The monthly salaries of 55 workers of a factory are displayed in the following ogive. Answer the following. (i) How many workers have a monthly salary UNDER $ 4000? (ii) How many workers have a monthly salarySun, 16 Sep 2018 16:50:28 -0400Sep 13, Problems on Frequency Polygon | Frequency Polygon Examples
https://www.math-only-math.com/problems-on-frequency-polygon.html0eb5ee24ed7762941d11794ec0a077c7We will discuss here some of the problems on frequency polygon. 1. The frequency polygon of a frequency distribution is shown below. Answer the following about the distribution from the histogram. (i) What is the frequency of the class interval whose class mark is 15?Thu, 13 Sep 2018 17:32:29 -0400Sep 11, Problems on Histogram | Reading Histograms | Histograms Examples
https://www.math-only-math.com/problems-on-histogram.html91f7dc3347e8622edb79ed87d169840aWe will discuss here some of the problems on histogram. The histogram for a frequency distribution is given below. (i) What is the frequency of the class interval 15 – 20? (ii) What is the class intervals having the greatest frequenciey? (iii) What is the cumulativeTue, 11 Sep 2018 19:24:18 -0400Sep 10, Cumulative-Frequency Curve | Ogive | Method of Constructing on Ogive
https://www.math-only-math.com/cumulative-frequency-curve.html57666fe0b662b8af82978230d396701bGropu data are also represented by a curve called ogive or cumulative-frequency curve. As the name suggests, in this representation cumulative frequencies of different class intervals play an important role. Method of Constructing on Ogive: Prepare a frequency-distributionMon, 10 Sep 2018 18:39:14 -0400Aug 28, Method of Constructing Frequency Polygon with the Help of Class Marks
https://www.math-only-math.com/frequency-polygon-with-the-help-of-a-class-marks.htmlcf9a47a696862446b0a9573afa32024aWe will discuss about the method of constructing a frequency polygon with the help of a class marks. Step I: Prepare a frequency-distribution table overlapping intervals. Step II: Find the class marks of the class intervals and locate them on the horizontal axisTue, 28 Aug 2018 19:23:50 -0400Aug 25, Method of Constructing a Frequency Polygon with the Help of Histogram
https://www.math-only-math.com/frequency-polygon-with-the-help-of-a-histogram.html54c9051684982c3c04d35cb02855f44bStep I: Draw the histogram for the frequency distribution as explained above. Step II: Locate the midpoint of the top horizontal side of each rectangle in the histogram. Step III: Locate the middle points on the horizontal axis of two imaginary intervals of common size, oneSat, 25 Aug 2018 16:47:55 -0400Aug 24, Frequency Polygon | Methods of Constructing a Frequency Polygon
https://www.math-only-math.com/frequency-polygon.html48f086b9402029b18d70f7e1079dd00eGrouped data are also represented by frequency polygons. A frequency polygon is a polygon whose vertices are at the midpoint of the tops of rectangles forming the histogram of the frequency distribution. These middle points correspond to the class marks of the correspondingFri, 24 Aug 2018 15:34:26 -0400Aug 22, Histogram | Method of Constructing a Histogram | Creating a Histogram
https://www.math-only-math.com/histogram.htmlfe1d5ddfc1a9fc00fa1ff0d8eb282ab7Grouped data are often represented graphically by histograms. A histogram consists of rectangles, each of which has breadth equal or proportional to the size of the concerned call interval, and height equal or proportional to the corresponding frequency.Wed, 22 Aug 2018 19:32:39 -0400Aug 20, Word Problems on Addition and Subtraction | Mixed Add & Subtract
https://www.math-only-math.com/word-problems-on-addition-and-subtraction.htmlc2bfae42248ab6489e5e53afe96c8390Solved examples on Word problems on addition and subtraction . 1. In a school there are 2,392 boys and 2,184 girls. Find the total number of students in the school. Solution: Number of boys in the school = 2392 Number of girls in the school = + 2184 Total students in theMon, 20 Aug 2018 15:11:20 -0400Aug 6, Worksheet on Word problem on Multiplication | Multiplication Facts
https://www.math-only-math.com/worksheet-on-word-problem-on-multiplication.htmlf0c8f3c44ba19bff753df3515c2ca138Practice the worksheet on word problem on multiplication. 1. One complete set of class IV costs $264. How much money did a class of 42 children pay to the bookshop owner, if all of them bought their books from him? 2. One pair of football shoes costs $ 628. Find the cost ofMon, 6 Aug 2018 16:43:14 -0400Jul 27, Word Problems on Multiplication |3rd Grade Math|Multiplication Problem
https://www.math-only-math.com/word-problem-on-multiplication.html472ce3f68c9f49337fcac4139aefcbb3Solved examples on word problems on multiplication.For a school trip 6 buses were hired. Each bus carried 42 children. How many children went on the trip? Solution: 2. The product of two numbers is 96. If one number is 8, find the other. Multiplicand × Multiplier = Product`Fri, 27 Jul 2018 12:26:43 -0400Jul 25, Worksheet on Word Problem on Addition and Subtraction | Answers
https://www.math-only-math.com/worksheet-on-word-problem-on-addition-and-subtraction.html406863fe364b1cf80d6f9378799e6f92Practice the worksheet on word problem on addition and subtraction. 1. In a village, there are 4,318 men, 3,624 women and 5,176 children. What is the total population of the village? 2. In a school, there are 860 children in the pre-primary section, 1,200 children in thWed, 25 Jul 2018 15:09:02 -0400Jul 24, Making the Numbers From Given Digits | Write Smallest/Greatest Number
https://www.math-only-math.com/making-the-numbers-from-given-digits.html186685224e854b9947dba3026ff620a1We can make numbers from the given digits. Let us see the rules. Rule I. To get the smallest number, arrange the digits in ascending order from left to right. Rule II. To get the greatest number, arrange the digits in descending order from left to right. Example: Write theTue, 24 Jul 2018 15:59:11 -0400Jul 13, Worksheet on Facts about Division | Division with Small Numbers
https://www.math-only-math.com/worksheet-on-facts-about-division.htmlac54531da82766642f4b475ac573ecf8Practice the worksheet on facts about division. We know, dividend is always equal to the product of the divisor and the quotient added to the remainder. This will help us to solve the given questions. 1. Fill in the blanks: (i) Division is __ subtraction.Fri, 13 Jul 2018 15:52:52 -0400Jul 13, Worksheet on Facts about Multiplication | Multiplication Sum | Answers
https://www.math-only-math.com/worksheet-on-facts-about-multiplication.html1c2598041d767903cf330ffdd9a9bca2Practice the worksheet on facts about multiplication. We know in multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the multiplier. This will help us to solve the given questions.Fri, 13 Jul 2018 15:39:08 -0400Jul 12, Worksheet on Facts about Subtraction | Subtraction with Small Numbers
https://www.math-only-math.com/worksheet-on-facts-about-subtraction.html013b49484bfee5d7e0e0694bf05dfa9fPractice the worksheet on facts about subtraction. Subtraction with small numbers can be worked out horizontally and subtraction with large numbers is worked out vertically. 1. Fill in the missing numbers. (i) Take away 14 from 80 is ______ (ii) 150 decreased by 80 is ____Thu, 12 Jul 2018 16:49:09 -0400Jul 12, Worksheet on Facts about Addition | Addition of Small Numbers
https://www.math-only-math.com/worksheet-on-facts-about-addition.html27fddcca8eb37c2693ae10a2b5a2e7d5Practice the worksheet on facts about addition. Addition of small numbers can be done horizontally and large numbers are added in vertical columns. 1. Fill in the missing number/word. (i) 4315 + 101 = 101 + ______ = ______ (ii) 1795 + 241 = 241 + ______Thu, 12 Jul 2018 15:56:45 -0400Jul 12, Facts about Multiplication | Multiplication Operation | Multiplicand
https://www.math-only-math.com/facts-about-multiplication.html6a3f4cbcb978056e68c02dc3877c2347We have learnt multiplication of numbers with 2digit multiplier. Now, we will learn more. Let us know some facts about multiplication. 1. In multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called theThu, 12 Jul 2018 15:42:10 -0400Jul 11, Facts about Subtraction | Subtraction of Small Numbers|Solved Examples
https://www.math-only-math.com/facts-about-subtraction.html2b05a7e37a760df1e5dcba90df17ce7fThe operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction with small numbers can be worked out horizontally. Example: 8 – 5 = 3 24 – 4 =Wed, 11 Jul 2018 17:41:47 -0400Jul 11, Facts about Addition|Addition of Small Numbers|Add 4 & 5-digit Numbers
https://www.math-only-math.com/facts-about-addition.html36ff8dc1d885ac50b1b72f841c86bdd7The operation to find the total of different values is called addition. Let us know some facts about addition which will help us to learn to add 4-digit and 5-digit numbers. 1. Addition of small numbers can be done horizontally. Example: 6 + 2 + 3 = 11Wed, 11 Jul 2018 16:01:52 -0400Jul 10, Facts about Division | Basic Division Facts | Learn Long Division
https://www.math-only-math.com/facts-about-division.html604f7644a4e743327fac817c5f9a08b7We have already learned division by repeated subtraction, equal sharing/distribution and by short division method. Now, we will read some facts about division to learn long division. 1. If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’.Tue, 10 Jul 2018 15:39:01 -0400Jul 7, Expanded Form and Short Form of a Number | Numbers in Expanded Form
https://www.math-only-math.com/expanded-form-and-short-form-of-a-number.html04526b10014b717e88e0e9c7901da876When we write a number as a sum of place value of its digits, the number is said to be in expended form and when we write a number using digits, the number is said to be in short form. There are 3 ways to write the expanded form. There are 3 ways to write the expanded formSat, 7 Jul 2018 17:31:31 -0400Jul 1, Long Division | Division by One-Digit Divisor and Two-Digit Divisors
https://www.math-only-math.com/long-division.html1594f4e13ddfde58f1248c4f73aeb4d2As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.Sun, 1 Jul 2018 15:59:27 -0400Jun 25, Multiplication of Matrices | How to Multiply Matrices? |Rules|Examples
https://www.math-only-math.com/multiplication-of-matrices.html5ab21c7a924bc72b1dd4670be98eec63Two matrices A and B are said to be conformable for the product AB if the number of columns of A be equal to the number of rows of B. If A be an m × n matrix and B an n × p matrix then their product AB is defined to be the m × p matrix whose (ij)th element is obtained byMon, 25 Jun 2018 17:25:14 -0400Jun 10, Worksheet on Addition of Matrices | Find the Sum of Two Matrices | Ans
https://www.math-only-math.com/worksheet-on-addition-of-matrices.html01881729b7c02f25469d80432d308bc8Practice the problems given in the worksheet on addition of matrices. If M and N are the two matrices of the same order, then the matrices are said conformable for addition, and their sum is obtained by adding the corresponding elements of M and N. 1. Find the sum of A and BSun, 10 Jun 2018 16:34:24 -0400Jun 9, Properties of Scalar Multiplication of a Matrix |Scalar Multiplication
https://www.math-only-math.com/properties-of-scalar-multiplication-of-a-matrix.html2afda6b339e0b8e774c8e38fec27d41aWe will discuss about the properties of scalar multiplication of a matrix. If X and Y are two m × n matrices (matrices of the same order) and k, c and 1 are the numbers (scalars). Then the following results are obvious. I. k(A + B) = kA + kB II. (k + c)A = kA + cA III. k(cA)Sat, 9 Jun 2018 16:11:24 -0400Jun 7, Scalar Multiplication of a Matrix | Examples on Scalar Multiplication
https://www.math-only-math.com/scalar-multiplication-of-a-matrix.html8eb7afeb9c6232580b9a5b1a896abf68The operation of multiplying variables by a constant scalar factor may properly be called scalar multiplication and the rule of multiplication of matrix by a scalar is that the product of an m × n matrix A = [aij] by a scalar quantity c is the m × n matrix [bij] where bijThu, 7 Jun 2018 19:24:55 -0400Jun 6, Subtraction of Matrices | Examples on Difference of Two Matrices
https://www.math-only-math.com/subtraction-of-matrices.html38455fb316ea9dfe34226cdc72f0df53We proceed to develop the algebra of subtraction of matrices. Two matrices A and B are said to be conformable for subtraction if they have the same order (i.e. same number of rows and columns) and their difference A - B is defined to be the addition of A and (-B).Wed, 6 Jun 2018 17:25:38 -0400Jun 5, Properties of Addition of Matrices | Commutative Law | Associative Law
https://www.math-only-math.com/properties-of-addition-of-matrices.html9af809c96af9a47a61b898f760dc34eaWe will discuss about the properties of addition of matrices. 1. Commutative law of addition of matrix: Matrix multiplication is commutative. This says that, if A and B are matrices of the same order such that A + B is defined then A + B = B + A. Proof: Let A = [aij]m × nTue, 5 Jun 2018 15:30:18 -0400Jun 4, Addition of Matrices | Example on Sum of Two Matrices
https://www.math-only-math.com/addition-of-matrices.html445dfaf5ee202f0cc7c583fe820bba6eWe proceed to develop the algebra of matrices. Two matrices A and B are said to be conformable for addition if they have the same order (same number of rows and columns). If A = (aij)m, n and B = (bij)m,n then their sum A + B is the matrix C = (cij)m,n where cij = aij + bijMon, 4 Jun 2018 17:10:13 -0400Jun 1, Triangular Matrix | Upper Triangular Matrix | Lower Triangular Matrix
https://www.math-only-math.com/triangular-matrix.html2a781f50a73f56c8808939395e37e745There are two types of triangular matrices. 1. Upper Triangular Matrix: A square matrix (aij) is said to be an upper triangular matrix if all the elements below the principal diagonal are zero (0). That is, [aij]m × n is an upper triangular matrix if (i) m = n and (ii) aijFri, 1 Jun 2018 18:50:44 -0400May 29, Height and Distance with Two Angles of Elevation | Solved Problems
https://www.math-only-math.com/height-and-distance-with-two-angles-of-elevation.html11feae3d5402c51bbaccd75b295f0152We will solve different types of problems on height and distance with two angles of elevation. Another type of case arises for two angles of elevations. In the given figure, let PQ be the height of pole of ‘y’ units. QR be the one of the distance between the foot of the poleTue, 29 May 2018 19:03:57 -0400May 22, Angle of Elevation | How to Find out the Angle of Elevation
https://www.math-only-math.com/angle-of-elevation.htmlbb067c5ec3a38ec678f4e693c0fbd14fWe have already learnt about trigonometry in previous units in detail. Trigonometry has its own applications in mathematics and in physics. One such application of trigonometry in mathematics is “height and distances”. To know about height and distances, we have to startTue, 22 May 2018 18:22:50 -0400May 20, Identity Matrix | Unit Matrix |If [d] is a scalar matrix then [d] = dI
https://www.math-only-math.com/identity-matrix.html222210823322c632c1c2bcd89718fbb4A scalar matrix whose diagonal elements are all equal to 1, the identity element of the ground field F, is said to be an identity (or unit) matrix. The identity matrix of order n is denoted by In. A scalar matrix is said to be a unit matrix, if diagonal elements are unity. Sun, 20 May 2018 18:35:31 -0400May 17, Definition of Equal Matrices | Examples of Equal Matrices
https://www.math-only-math.com/equal-matrices.html22c25f427e3f52494a6e4a87ada3bbc1Equality of two matrix: Two matrices [aij] and [bij] are said to be equal when they have the same number of rows and columns and aij = bij for all admissible values of i and j. Definition of Equal Matrices: Two matrices A and B are said to be equal if A and B have the sameThu, 17 May 2018 18:16:28 -0400May 10, Null Matrix | Null or Zero Matrix|Zero Matrix|Problems on Null Matrix
https://www.math-only-math.com/null-matrix.html2caad544829b14521a6dbfd5a51dc80eIf each element of an m × n matrix be 0, the null element of F, the matrix is said to be the null matrix or the zero matrix of order m × n and it is denoted by Om,n. It is also denoted by O, when no confusion regarding its order arises. Null or zero Matrix: Whether A is aThu, 10 May 2018 16:39:03 -0400May 7, Column Matrix | Definition of Column Matrix |Examples of Column Matrix
https://www.math-only-math.com/column-matrix.html3629824d939a61f125fd89fb606fb75eHere we will discuss about the column matrix with examples. In an m × n matrix, if n = 1, the matrix is said to be a column matrix. Definition of Column Matrix: If a matrix have only one column then it is called column matrix. Examples of column matrix:Mon, 7 May 2018 16:24:13 -0400May 3, Row Matrix | Definition of Row Matrix | Examples of Row Matrix
https://www.math-only-math.com/row-matrix.htmla92d0bb38751d4cb4c45788dd7e15a6dIn an m × n matrix, if m = 1, the matrix is said to be a row matrix. Definition of Row Matrix: If a matrix have only one row then it is called row matrix. Here we will discuss about the row matrix with examples. Examples of row matrix: Thu, 3 May 2018 18:42:00 -0400Apr 25, Square Matrix | Definition of Square Matrix |Diagonal of Square Matrix
https://www.math-only-math.com/square-matrix.htmlcc88e174bc09f2930402240d5c2eef31If square matrixes have n rows or columns then the matrix is called the square matrix of order n or an n-square matrix. Definition of Square Matrix: An n × n matrix is said to be a square matrix of order n. In other words when the number of rows and the number of columns inWed, 25 Apr 2018 18:57:13 -0400Apr 25, Matrix | Definition of a Matrix | Examples of a Matrix | Elements
https://www.math-only-math.com/matrix.htmla2b51f377bcbdb7b2376b213a01fe23eA rectangular array of mn elements aij into m rows and n columns, where the elements aij belongs to field F, is said to be a matrix of order m × n (or an m × n matrix) over the field F. Definition of a Matrix: A matrix is a rectangular arrangement or array of numbersWed, 25 Apr 2018 17:53:52 -0400Mar 30, Joint Variation | Solving Joint Variation Problems and Application
https://www.math-only-math.com/joint-variation.html1d53c5980c0c9a922c736c90234e8c36One variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product. If the variable A varies directly as the product of the variables B, C and D, i.e., if.A ∝ BCD or A = kBCD (k = constant ), then A varies jointlyFri, 30 Mar 2018 19:32:26 -0400