Chapter 16.2, Problem 14WE

To determine

To simplify: the given expression.

Answer to Problem 14WE

The sum is $\left[\begin{array}{c}6\\ 36\\ 30\end{array}\right]$ .

Explanation of Solution

Given information:

Given expression,

  $3\left[\begin{array}{c}2\\ 2\\ 5\end{array}\right]+5\left[\begin{array}{c}0\\ 6\\ 3\end{array}\right]$

Calculation: Consider the givn expression,

  $3\left[\begin{array}{c}2\\ 2\\ 5\end{array}\right]+5\left[\begin{array}{c}0\\ 6\\ 3\end{array}\right]$

Now, solve the expression as shown,

  $\begin{array}{c}3\left[\begin{array}{c}2\\ 2\\ 5\end{array}\right]+5\left[\begin{array}{c}0\\ 6\\ 3\end{array}\right]=\left[\begin{array}{c}3\cdot 2\\ 3\cdot 2\\ 3\cdot 5\end{array}\right]+\left[\begin{array}{c}5\cdot 0\\ 5\cdot 6\\ 5\cdot 3\end{array}\right]\\ =\left[\begin{array}{c}6\\ 6\\ 15\end{array}\right]+\left[\begin{array}{c}0\\ 30\\ 15\end{array}\right]\\ =\left[\begin{array}{c}6+0\\ 6+30\\ 15+15\end{array}\right]\\ =\left[\begin{array}{c}6\\ 36\\ 30\end{array}\right]\end{array}$

Hence the sum is $\left[\begin{array}{c}6\\ 36\\ 30\end{array}\right]$ .