Chapter 12, Problem 7CR

To determine

To simplify: the matrix using scalar matrix multiplication.

Answer to Problem 7CR

  $\left[\begin{array}{ccc}-3& -6& 3\\ 0& 6& -9\\ 9& -3& 0\end{array}\right]$ .

Explanation of Solution

Given:

  $-3\left[\begin{array}{ccc}1& 2& -1\\ 0& -2& 3\\ -3& 1& 0\end{array}\right]$ .

Concept used:

Scalar multiplication and matrix multiplication:

just take a regular number called a scalar and multiply it on every entry in the matrix.

Calculation:

  $-4.2\left[\begin{array}{cc}3& 1.1\\ 3& -2\\ -1& 2.9\end{array}\right]$ .

Multiply each Elements by the scalar.

  $\Rightarrow \left[\begin{array}{cc}\left(-4.2\right)\times 3& \left(-4.2\right)\times 1.1\\ \left(-4.2\right)\times 3& \left(-4.2\right)\times \left(-2\right)\\ \left(-4.2\right)\times \left(-1\right)& \left(-4.2\right)\times 2.9\end{array}\right]$ .

  $\Rightarrow \left[\begin{array}{cc}-12.6& -4.2\\ -12.6& 8.4\\ 4.2& 12.18\end{array}\right]$

Hence, the matrices after multiply by scalar is $\left[\begin{array}{cc}-12.6& -4.2\\ -12.6& 8.4\\ 4.2& 12.18\end{array}\right]$ .