Chapter 12.1, Problem 2P

a.

To determine

To find: the product of the given matrix.

Answer to Problem 2P

  $-2\left[37.55\right]=\left[-6-15-10\right]$ .

Explanation of Solution

Given:

The given matrix is $-2\left[37.55\right]$ .

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 $-2\left[37.55\right]$ .

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

Therefore, multiply the matrix. Now,

  $\begin{array}{l}-2\left[37.55\right]=\left[-2\times 3-2\times 7.5-2\times 5\right]\\ =\left[-6-15-10\right]\end{array}$

Hence, the multiplication of the given matrix is $-2\left[37.55\right]=\left[-6-15-10\right]$ .

b.

To determine

To find: the product of the given matrix.

Answer to Problem 2P

  $1.5\left[\begin{array}{l}-113\\ 0-1.5\end{array}\right]=\left[\begin{array}{l}-16.54.5\\ 0-2.25\end{array}\right]$ .

Explanation of Solution

Given:

The given matrix is $1.5\left[\begin{array}{l}-113\\ 0-1.5\end{array}\right]$ .

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 $1.5\left[\begin{array}{l}-113\\ 0-1.5\end{array}\right]$ .

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

Therefore, multiply the matrix. Now,

  $\begin{array}{l}1.5\left[\begin{array}{l}-113\\ 0-1.5\end{array}\right]=\left[\begin{array}{l}1.5\times \left(-11\right)1.5\times 3\\ 1.5\times 01.5\times \left(-1.5\right)\end{array}\right]\\ =\left[\begin{array}{l}-16.54.5\\ 0-2.25\end{array}\right]\end{array}$

Hence, the multiplication of the given matrix is $1.5\left[\begin{array}{l}-113\\ 0-1.5\end{array}\right]=\left[\begin{array}{l}-16.54.5\\ 0-2.25\end{array}\right]$ .