Chapter 16.2, Problem 12OE

To determine

To simplify: the given expression.

Answer to Problem 12OE

The difference is $\left[\begin{array}{ccc}-15& 0& 5\\ -30& -10& -20\end{array}\right]$ .

Explanation of Solution

Given information:

Given expression,

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

Calculation:

  $O_{2\times 3}$ is a zero matrix with 2 rows and 3 columns.

  $\begin{array}{c}{O}_{2\times 3}-5\left[\begin{array}{ccc}3& 0& -1\\ 6& 2& 4\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\end{array}\right]-\left[\begin{array}{ccc}5\cdot 3& 5\cdot 0& 5\cdot \left(-1\right)\\ 5\cdot 6& 5\cdot 2& 5\cdot 4\end{array}\right]\\ =\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\end{array}\right]-\left[\begin{array}{ccc}15& 0& -5\\ 30& 10& 20\end{array}\right]\\ =\left[\begin{array}{ccc}0-15& 0-0& 0-\left(-5\right)\\ 0-30& 0-10& 0-20\end{array}\right]\\ =\left[\begin{array}{ccc}-15& 0& 5\\ -30& -10& -20\end{array}\right]\end{array}$

Hence, the difference is $\left[\begin{array}{ccc}-15& 0& 5\\ -30& -10& -20\end{array}\right]$ .