HOW TO FIND THE ORDER OF PRODUCT OF TWO MATRICES

How to Find the Order of Product of Two Matrices ?

Here we are going to see how to find the order of product of two matrices.

How to Find the Order of Product of Two Matrices ?

To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Consider the multiplications of 3×3 and 3×2 matrices.

(Order of left hand matrix) x (order of right hand matrix) -> (order of product matrix).

(3 × 3 ) x (3 × 2 ) -> (3 × 2 )

The product AB can be found if the number of columns of matrix A is equal to the number of rows of matrix B. If the order of matrix A is m x n and B is n x p then the order of AB is m x p .

Question 1 :

Find the order of the product matrix AB if Solution :

(i)  Order of A is 3 x 3, order of B is 3 x 3.

The order of the matrix AB is 3 x 3.

(ii)  Order of A is 4 x 3, order of B is 3 x 2.

The order of the matrix AB is 4 x 2.

(iii)  Order of A is 4 x 2, order of B is 2 x 2.

The order of the matrix AB is 4 x 2.

(iv)  Order of A is 4 x 5, order of B is 5 x 1.

The order of the matrix AB is 4 x 1.

(v)  Order of A is 1 x 1, order of B is 1 x 3.

The order of the matrix AB is 1 x 3.

Question 2 :

If A is of order p x q and B is of order q x r what is the order of AB and BA?

Solution :

(p x q) (q x r)  =  p x r

The order of matrix AB is p x r.

(q x r) (p x q)   =  p x r

The product of matrices B and A is not possible.

Hence it is not defined.

Question 3 :

A has ‘a’ rows and ‘a + 3 ’ columns. B has ‘b’ rows and ‘17–b’ columns, and if both products AB and BA exist, find a, b?

Solution :

Number of rows of A = a

Number of columns of A = a + 3

Number of rows of B = b

Number of columns of A = 17 - b

Since the product of matrices A and B is possible,

[a x (a + 3)] [b x (17 - b)]

a + 3  =  b

a - b  =  -3  -----(1)

Since the product of matrices B and A is possible,

[b x (17 - b)]  [a x (a + 3)]

17 - b  =  a

a + b  =  17 ----(2)

(1) + (2)

2a  =  14

a  =  7

By applying the value of a in (1), we get

7 - b = -3

-b  =  -3 - 7

-b  =  -10

b = 10 After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Order of Product of Two Matrices".

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