Chapter 6.6, Problem 29PPS

To determine

To perform: the indicated matrix operations.

Answer to Problem 29PPS

Therefore, order of the matrices are not same, thus it is impossible to perform operation.

Explanation of Solution

Given:

  $-3\left[\begin{array}{c}7\\ -4\\ -2\\ 1\end{array}\right]-2\left[\begin{array}{c}7\\ -5\\ -3\end{array}\right]$

Calculation:

Objective: To perform the indicated operation $-3\left[\begin{array}{c}7\\ -4\\ -2\\ 1\end{array}\right]-2\left[\begin{array}{c}7\\ -5\\ -3\end{array}\right]$ or to explain why the operation is not possible.

To subtract two matrices, we have to subtract corresponding components of the matrices. Thus if we want to subtract two matrices then the order of the matrices must be same

  $\begin{array}{l}\left[\begin{array}{c}7\\ -4\\ -2\\ 1\end{array}\right]4\text{ rows}\\ \text{1 column}\end{array}$

Matrix has 4 rows and 1 column. Therefore, it is a $\text{4}\times \text{1}$ matrix.

  $\begin{array}{l}\left[\begin{array}{c}7\\ -5\\ -3\end{array}\right]3\text{ rows}\\ \text{1 column}\end{array}$

Matrix has 3 rows and 1 column. Therefore, it is a $\text{3}\times \text{1}$ matrix

Conclusion:

Therefore, order of the matrices are not same, thus it is impossible to perform operation.