Chapter 7.5, Problem 107E

To determine

To state: that whether the matrices are of proper dimension to perform the operation $D\left(A-3B\right)$ .

Answer to Problem 107E

the operation $D\left(A-3B\right)$ can be perform and The dimension of the resultant of the operation $D\left(A-3B\right)$ is $2\times 3$ .

Explanation of Solution

the operation $D\left(A-3B\right)$ can be perform and The dimension of the resultant of the operation $D\left(A-3B\right)$ is $2\times 3$ .

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 subtraction matrices the order of both matrices must be same.

Since to perform the operation $A-3B$ , the order of matrices $A,3B$ must be same,

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

The dimension of the resultant of the operation $A-3B$ is $2\times 3$ .

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 $D\left(A-3B\right)$ , the number of columns of matrices $D$ must be same with the number of rows of matrices $A-3B$ .

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

Thus, the operation $D\left(A-3B\right)$ can be perform.

The dimension of the resultant of the operation $D\left(A-3B\right)$ is $2\times 3$ .