Chapter 16.2, Problem 11OE

To determine

To simplify: the given expression.

Answer to Problem 11OE

The sum is $\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]$ .

Explanation of Solution

Given information:

Given expression,

  $O_{2\times 3}+\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]$

Calculation:$O_{2\times 3}$ is a zero matrix with 2 rows and 3 columns. For each set of $m\times n$ matrices, $O_{m\times n}$ is the identity for addition.

  $\begin{array}{c}{O}_{2\times 3}+\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\end{array}\right]+\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]\\ =\left[\begin{array}{ccc}0+3& 0+5& 0+2\\ 0+\left(-2\right)& 0+8& 0+0\end{array}\right]\\ =\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]\end{array}$

Hence, the sum is $\left[\begin{array}{ccc}3& 5& 2\\ -2& 8& 0\end{array}\right]$ .