Chapter 7.5, Problem 103E

To determine

To state: that whether the matrices are of proper dimension to perform the operation $CD$ .

Answer to Problem 103E

the operation $CD$ can be perform and The dimension of the resultant of the operation $CD$ is $\text{3}\times 2$ .

Explanation of Solution

Given information :

The dimension of matrices $A,B,C,D$ respectively are $2\times 3,2\times 3,3\times 2,2\times 2$ .

by the definition of multiplication matrices the number of columns of first matrices must be the same with the number of rows of second matrices.

Since to perform the operation $CD$ , the number of columns of matrices $C$ must be same with the number of rows of matrices $D$ .

Here, the order of matrices $C\text{ and }D$ are $3\times 2\text{ and 2}\times 2$ .

Thus, the operation $CD$ can be perform.

The dimension of the resultant of the operation $CD$ is $\text{3}\times 2$ .