Chapter 4, Problem 10MCQ

To determine

Tofind:the product of the two matrices.

Answer to Problem 10MCQ

The product of two matrices is $\left[\begin{array}{ccc}-6& 17& 4\\ 3& 29& -32\end{array}\right]$ .

Explanation of Solution

Given:

  $\left[\begin{array}{cc}-2& 3\\ 1& 6\end{array}\right].\left[\begin{array}{ccc}3& -1& 4\\ 0& 5& -6\end{array}\right]$

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:

  $\left[\begin{array}{cc}-2& 3\\ 1& 6\end{array}\right]\left[\begin{array}{ccc}3& -1& 4\\ 0& 5& -6\end{array}\right]$ .

  $\left[\begin{array}{cc}-2& 3\\ 1& 6\end{array}\right]\left[\begin{array}{ccc}3& -1& 4\\ 0& 5& -6\end{array}\right]=\left[\begin{array}{ccc}-6+0& 2+15& -8+12\\ 3+0& -1+30& 4-36\end{array}\right]=\left[\begin{array}{ccc}-6& 17& 4\\ 3& 29& -32\end{array}\right]$ .

Hence, the product of two matrices is $\left[\begin{array}{ccc}-6& 17& 4\\ 3& 29& -32\end{array}\right]$ .