Chapter 12, Problem 26MCQ

Solution

To find: The dimensions of the required matrix.

The dimensions of the other matrix is $5\times 3$

Given information:

Given,the product of two matrices has dimensions $4\times 3$ . And one of the matrices in the multiplication has the dimensions $4\times 5$ .

Calculation:

Two matrices can be multiplied when the number of columns of the first matrix is equal to number of rows of second matrix.

i.e., if X is a $a\times b$ matrix and Y is a $c\times d$ matrix, then the multiplication XY is possible if and only if $b=c$ and the dimension of the resultant matrix is $a\times d$

Here the rows of the resultant matrix is same as rows of one of the given matrices. Hence, given matrix is the first matrix which can be represented as $\left(4\times 5\right)\times \left(x\times y\right)=\left(4\times 3\right)$

The multiplication is possible only if the columns of the first matrix is same as rows of second matrix. And the columns of the resultant matrix is same as columns of the second matrix.

Hence, $x=5,y=3$

The dimensions of the other matrix is $5\times 3$

Conclusion:

The dimensions of the other matrix is $5\times 3$