Chapter 6.8, Problem 59SR

To determine

the given operations

Answer to Problem 59SR

The result is $\left[\begin{array}{ccc}-6& -18& -2\\ 6& -10& 6\\ -2& -4& -12\end{array}\right]$

Explanation of Solution

Given:

If $A=\left[\begin{array}{ccc}4& 5& 6\\ 0& -1& -3\\ 2& -3& 7\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& 9& 1\\ -3& 5& -3\\ 1& 2& 6\end{array}\right]$

  $-2B$

Calculation:

Here the matrices are:

  $A=\left[\begin{array}{ccc}4& 5& 6\\ 0& -1& -3\\ 2& -3& 7\end{array}\right],B=\left[\begin{array}{ccc}3& 9& 1\\ -3& 5& -3\\ 1& 2& 6\end{array}\right]$

The strategy is to find $-2B$ .

The value of the expression can be found as below.

  $\begin{array}{l}-2B=-2\left[\begin{array}{ccc}3& 9& 1\\ -3& 5& -3\\ 1& 2& 6\end{array}\right]\\ =\left[\begin{array}{ccc}-2.3& -2.9& -2.1\\ -2.\left(-3\right)& -2.5& -2.\left(-3\right)\\ -2.1& -2.2& -2.6\end{array}\right]\\ =\left[\begin{array}{ccc}-6& -18& -2\\ 6& -10& 6\\ -2& -4& -12\end{array}\right]\end{array}$

Hence, the result is $\left[\begin{array}{ccc}-6& -18& -2\\ 6& -10& 6\\ -2& -4& -12\end{array}\right]$

Conclusion:

Hence, the result is $\left[\begin{array}{ccc}-6& -18& -2\\ 6& -10& 6\\ -2& -4& -12\end{array}\right]$