Chapter SH, Problem 3.12EP

To determine

To express: the total number of new car models of each color after the lots are combined as a matrix.

Answer to Problem 3.12EP

  $\left[\begin{array}{l}81010\\ 1468\\ 12127\end{array}\right]$ .

Explanation of Solution

Given:

A car dealer ship is combining two of their lots. That is

  $\text{Lot}1=\left[\begin{array}{l}157\\ 843\\ 652\end{array}\right]$ , and $\text{Lot}2=\left[\begin{array}{l}753\\ 625\\ 675\end{array}\right]$

Calculation:

Consider the matrices that represent the number of new car models of each color of two different lots:

  $\text{Lot}1=\left[\begin{array}{l}157\\ 843\\ 652\end{array}\right]$ , and $\text{Lot}2=\left[\begin{array}{l}753\\ 625\\ 675\end{array}\right]$

The total number of new car models of each color after the lots are combined will be computed by adding two given matrices. Do the matrix addition as follows:

  $\begin{array}{l}\text{Lot}1+\text{Lot}2=\left[\begin{array}{l}157\\ 843\\ 652\end{array}\right]+\left[\begin{array}{l}753\\ 625\\ 675\end{array}\right]\\ =\left[\begin{array}{l}1+75+57+3\\ 8+64+23+5\\ 6+65+72+5\end{array}\right]\\ =\left[\begin{array}{l}81010\\ 1468\\ 12127\end{array}\right]\end{array}$

Therefore, the matrix that represents the total number of new car models of each color after the lots are combined will be, $\left[\begin{array}{l}81010\\ 1468\\ 12127\end{array}\right]$