Chapter 7.5, Problem 111E

a.

To determine

To state: that is it possible that $A=B$ .

Answer to Problem 111E

No, it is not possible to $A=B$ .

Explanation of Solution

Given information :

Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ .

since, Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ ,

So there order are not same.

Thus $A\ne B$ .

b.

To determine

To state: that $A+B$ is defined or not.

Answer to Problem 111E

No, $A+B$ is not defined.

Explanation of Solution

Given information :

Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ .

since, Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ ,

By definition of adding matrices, the order of both matrices must be same .

Thus, $A+B$ is not defined.

c.

To determine

To state: that $AB$ is defined or not.

Answer to Problem 111E

yes, $AB$ is defined.

Explanation of Solution

Given information :

Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ .

since, Matrices $A$ and $B$ be of dimensions $3\times 2$ and $2\times 2$ ,

By definition of multiplication matrices, the number of columns of first matrices must be the same to the other matrices row number.

Thus, $AB$ is defined.