Chapter 4.8, Problem 75SR

To determine

To Find: The solution of the given matrix.

Answer to Problem 75SR

  $\left[\begin{array}{cc}-28& 60\\ 20& -70\end{array}\right]$

Explanation of Solution

Given:

  $-2\left[\begin{array}{cc}5& -9\\ 5& 11\end{array}\right]-6\left[\begin{array}{cc}3& -7\\ -5& 8\end{array}\right]$

Formula Used:

  $\begin{array}{l}\text{Distributive property }\\ a\left(b+c\right)=a.b+a.c\end{array}$

Calculation:

  $\begin{array}{l}-2\left[\begin{array}{cc}5& -9\\ 5& 11\end{array}\right]-6\left[\begin{array}{cc}3& -7\\ -5& 8\end{array}\right]\\ =\left[\begin{array}{cc}-10& 18\\ -10& -22\end{array}\right]-\left[\begin{array}{cc}18& -42\\ -30& 48\end{array}\right]\\ =\left[\begin{array}{cc}-10-18& 18+42\\ -10+30& -22-48\end{array}\right]\\ =\left[\begin{array}{cc}-28& 60\\ 20& -70\end{array}\right]\end{array}$

Conclusion:

Thus the product is $\left[\begin{array}{cc}-28& 60\\ 20& -70\end{array}\right]$