Chapter 4, Problem 11MCQ

To determine

Tofind:the product of the two matrices.

Answer to Problem 11MCQ

Theproduct is not possible.

Explanation of Solution

Given:

  $\left[\begin{array}{ccc}-4& 0& -1\\ 0& 1& 8\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& 4\end{array}\right]$

Concept used:

Product of the two matrices.

  $\left[\begin{array}{cc}{\text{a}}_{\text{11}}& {\text{a}}_{\text{12}}\\ {\text{a}}_{\text{21}}& {\text{a}}_{\text{22}}\end{array}\right].\left[\begin{array}{cc}{\text{b}}_{\text{11}}& {\text{b}}_{\text{12}}\\ {\text{b}}_{\text{21}}& {\text{b}}_{\text{22}}\end{array}\right]=\left[\begin{array}{cc}{a}_{11}{\text{b}}_{\text{11}}+{\text{a}}_{\text{12}}{\text{b}}_{\text{21}}& {\text{a}}_{\text{11}}{\text{b}}_{\text{12}}+{\text{a}}_{\text{12}}{\text{b}}_{\text{22}}\\ {\text{a}}_{\text{21}}{\text{b}}_{\text{11}}+{\text{a}}_{\text{22}}{\text{b}}_{\text{21}}& {\text{a}}_{\text{21}}{\text{b}}_{\text{12}}+{\text{a}}_{\text{22}}{\text{b}}_{\text{22}}\end{array}\right]$ .

Calculation:

  $\left[\begin{array}{ccc}-4& 0& -1\\ 0& 1& 8\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& 4\end{array}\right]$ .

The column of the first matrices is $3$ and row of the seconds matrices is $2$ therefore the matrices cannot be multiply.

Two multiply the two matrices column of the first matrices must equals to the raw of the second matrices.

Hence, the product is not possible.