Q17. - Algebra 1

Question

Perform the indicated matrix operations. If an operation cannot be performed, write impossible.

$\mathbf{-}\mathbf{2}\left[\begin{array}{cc}-2& 7\\ 6& -4\\ 8& 5\end{array}\right]$

Step-by-Step Solution

Answer

The result after performing the indicated matrix operations is $\left[\begin{array}{cc}4& -14\\ -12& 8\\ -16& -10\end{array}\right]$.

Step 1. Write the property of scalar multiplication of matrix.

The property of scalar multiplication of matrix states that:

The scalar multiplication of matrix $A$ with a scalar $k$ is given by:

$kA=k{\left[a_{ij}\right]}_{m\times n}={\left[k{a}_{ij}\right]}_{m\times n}$

That implies the scalar multiplication of the matrix with scalar can be obtained by multiplying every element of the matrix with scalar and the matrix obtained has same order as that of the matrix which is multiplied by the scalar.

Step 2. Perform the indicated matrix operations.

 

The result after the scalar multiplication of the given matrix is:

$\begin{array}{c}-2\left[\begin{array}{cc}-2& 7\\ 6& -4\\ 8& 5\end{array}\right]=\left[\begin{array}{cc}-2(-2)& -2\left(7\right)\\ -2\left(6\right)& -2(-4)\\ -2\left(8\right)& -2\left(5\right)\end{array}\right]\\ =\left[\begin{array}{cc}4& -14\\ -12& 8\\ -16& -10\end{array}\right]\end{array}$

Therefore, the result after performing the indicated matrix operations is $\left[\begin{array}{cc}4& -14\\ -12& 8\\ -16& -10\end{array}\right]$.