Chapter 7.5, Problem 100E

To determine

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

Answer to Problem 100E

the operation $CB-D$ can not be perform.

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 $CB$ , the number of columns of matrices $C$ must be same with the number of rows of matrices $A$ .

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

Thus, the operation $CB$ can be perform.

The dimension of the resultant of the operation $CB$ is $3\times 3$ .

by the definition of subtraction matrices the order of both matrices must be same.

Since to perform the operation $CB-D$ , the order of matrices $CB,D$ must be same,

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

Thus, the operation $CB-D$ cannot be perform.