# 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. ### Measuring Capacity | Standard Unit of Capacity | Litre | Millilitres

Nov 29, 23 01:15 AM

We will discuss about measuring capacity. The milkman measures milk in liters. Petrol is given in liters. Mobil oil is sold in liters. Two milk bottles contain 1 liter of milk. One milk bottle

2. ### Addition and Subtraction of Units of Measurement | Metric Units

Nov 29, 23 12:54 AM

We can add the units of measurement like decimal numbers. 1. Add 5 m 9 dm and 11 m and 5 dm Solution: 5 m 9 dm = 5.9 m 11 m 5 dm = 11.5 m Hence, 5 m 9 dm + 11 m 5 dm = 17 m 4 dm or 17.4 m 2. Add 15 cm…