# Problems on Understanding Matrices

Here we will solve different types of Problems on understanding matrices.

1. Let A = $$\begin{bmatrix} a & b\\ x & y \end{bmatrix}$$. Answer the following.

(i) What is the order of the matrix A?

(ii) Find (2, 1)th and (1, 2)th elements.

Solution:

(i) The order is 2 × 2 because there are 2 rows and 2 columns in the matrix.

(ii) (2, 1)th element = the number falling in the 2nd row and the 1st column = x.

(1, 2)th element = the number falling in the 1st row and the 2nd column = b.

2. If a matrix has eight elements, find the possible orders of the matrix.

Solution:

8 = 8 × 1, 8 = 1 × 8, 8 = 2 × 4, 8 = 4 × 2.

Therefore, the possible orders of the matrix are 8 × 1, 1 × 8, 2 × 4 and 4 × 2.

3. In the matrix $$\begin{bmatrix} -10 & 4\\ 3 & 7\\ -1 & 5 \end{bmatrix}$$, find the (2, 2)th, (3, 1)th and (1, 2)th elements.

Solution:

(2, 2)th element = the number falling in the 2nd row and the 2nd column = 7.

(3, 1)th element = the number falling in the 3rd row and the 1st column = -1.

(1, 2)th element = the number falling in the 1st row and the  2nd column = 4.

4. If A = B, where A = $$\begin{bmatrix} 3 & x + y\\ x - y & 5 \end{bmatrix}$$ and B = $$\begin{bmatrix} 3 & -7\\ 2 & 5 \end{bmatrix}$$ then find x and y.

Solution:

As A = B, the corresponding elements are equal. So, x + y = -7 and x – y = 2.

Adding the two equations we get, 2x = - 5.

Therefore, x = -$$\frac{5}{2}$$.

Again, subtracting the 2nd equation from the 1st equation we get, 2y = -9.

Therefore, y = -$$\frac{9}{2}$$.

From Problems on Understanding Matrices to HOME

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

2. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 13, 24 02:23 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

3. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 13, 24 01:20 AM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

4. ### Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers