Chapter 12.1, Problem 29P

Simplify each expression. (Hint: Multiply before adding or subtracting.)

$2\left[\begin{array}{l}-1-13\\ 461.5\\ 0-22.5\end{array}\right]+\left(-0.1\right)\left[\begin{array}{l}2.2-410\\ -1.63-1\\ 046.6\end{array}\right]$

To determine

Simplify given expression.

Answer to Problem 29P

  $\left[\begin{array}{l}\text{-2}\text{.22 -1}\text{.6 5}\\ \text{8}\text{.16 11}\text{.7 3}\text{.1}\\ \text{ 0 -4}\text{.4 4}\text{.34}\end{array}\right]$

Explanation of Solution

Given:

  $2\left[\begin{array}{l}\text{-1 -1 3}\\ \text{ 4 6 1}\text{.5}\\ \text{ 0 -2 2}\text{.5}\end{array}\right]-0.1\left[\begin{array}{l}2.2-4\text{ 10}\\ \text{-1}\text{.6 3 -1}\\ \text{0 4 6}\text{.6}\end{array}\right]$

Formula Used:

  $x\left[\begin{array}{l}\text{a b g}\\ \text{d e h}\\ \text{c f i}\end{array}\right]=\left[\begin{array}{l}\text{xa xb xg}\\ \text{xd xe xh}\\ \text{xc xf xi}\end{array}\right]$

  $\left[\begin{array}{l}\text{a b m}\\ \text{c d n}\\ \text{i j o}\end{array}\right]+\left[\begin{array}{l}\text{e f p}\\ \text{g h q}\\ \text{k l r}\end{array}\right]=\left[\begin{array}{l}\text{a+e b+f m+p}\\ \text{c+g d+h n+q }\\ \text{i+k j+l o+r}\end{array}\right]$

Calculation:

  $\begin{array}{l}2\left[\begin{array}{l}\text{-1 -1 3}\\ \text{ 4 6 1}\text{.5}\\ \text{ 0 -2 2}\text{.5}\end{array}\right]-0.1\left[\begin{array}{l}2.2-4\text{ 10}\\ \text{-1}\text{.6 3 -1}\\ \text{0 4 6}\text{.6}\end{array}\right]\\ =\left[\begin{array}{l}\text{-2 -2 6}\\ \text{ 8 12 3}\\ \text{ 0 -4 5}\end{array}\right]+\left[\begin{array}{l}\text{-0}\text{.22 0}\text{.4 -1}\\ \text{0}\text{.16 -0}\text{.3 0}\text{.1}\\ \text{0 -0}\text{.4 -0}\text{.66}\end{array}\right]\mathrm{..................}\left\{x\left[\begin{array}{l}\text{a b g}\\ \text{d e h}\\ \text{c f i}\end{array}\right]=\left[\begin{array}{l}\text{xa xb xg}\\ \text{xd xe xh}\\ \text{xc xf xi}\end{array}\right]\right\}\\ =\left[\begin{array}{l}\text{-2-0}\text{.22 -2+0}\text{.4 6-1}\\ \text{8+0}\text{.16 12-0}\text{.3 3+0}\text{.1}\\ \text{0+0 -4-0}\text{.4 5-0}\text{.66}\end{array}\right]\mathrm{...........................}\left\{\left[\begin{array}{l}\text{a b m}\\ \text{c d n}\\ \text{i j o}\end{array}\right]+\left[\begin{array}{l}\text{e f p}\\ \text{g h q}\\ \text{k l r}\end{array}\right]=\left[\begin{array}{l}\text{a+e b+f m+p}\\ \text{c+g d+h n+q }\\ \text{i+k j+l o+r}\end{array}\right]\right\}\\ =\left[\begin{array}{l}\text{-2}\text{.22 -1}\text{.6 5}\\ \text{8}\text{.16 11}\text{.7 3}\text{.1}\\ \text{ 0 -4}\text{.4 4}\text{.34}\end{array}\right]\end{array}$