Chapter 12.1, Problem 19PPE

To determine

To find: the multiplication of the given matrix.

Answer to Problem 19PPE

  $-3.1\left[\begin{array}{l}47.5\\ 9-5\\ 14.6\end{array}\right]=\left[\begin{array}{l}-12.4-23.25\\ -27.915.5\\ -3.114.26\end{array}\right]$ .

Explanation of Solution

Given:

The given matrix is $-3.1\left[\begin{array}{l}47.5\\ 9-5\\ 14.6\end{array}\right]$ .

Concept used:

Scalar multiplication of the matrix: scalar multiplication refers to the product of a real number and a matrix. In scalar multiplication, each element in the matrix is multiplied by the given scalar. 

Calculation:

The given matrix is $-3.1\left[\begin{array}{l}47.5\\ 9-5\\ 14.6\end{array}\right]$ .

Since, each element in the matrix is multiplied by the given scalar.

Therefore, multiply the matrix. Now,

  $\begin{array}{l}-3.1\left[\begin{array}{l}47.5\\ 9-5\\ 14.6\end{array}\right]=\left[\begin{array}{l}-3.1\times 4-3.1\times 7.5\\ -3.1\times 9-3.1\times \left(-5\right)\\ -3.1\times 1-3.1\times 4.6\end{array}\right]\\ =\left[\begin{array}{l}-12.4-23.25\\ -27.915.5\\ -3.114.26\end{array}\right]\end{array}$

Hence, the multiplication of the given matrix is $-3.1\left[\begin{array}{l}47.5\\ 9-5\\ 14.6\end{array}\right]=\left[\begin{array}{l}-12.4-23.25\\ -27.915.5\\ -3.114.26\end{array}\right]$ .