Question

Use matrices $A$, $B$, $C$and $D$to find the following.

$A=\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right],B=\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right],C=\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right],D=\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]$

$4C$

Short answer

The final matrix after performing the indicated matrix operations is $4C=\left[\begin{array}{cc}0& 16\\ -8& 20\\ 28& -4\end{array}\right]$.

Step-by-step solution

- Substitute the matrix

Substitute$\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right]$ for C into $4C$.

$4C=4\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right]$

- Perform the scalar multiplication

Scalar multiplication -The product of a scalar k and an $m\times n$ matrix is an $m\times n$ matrix in which each element equals k times the corresponding elements of the original matrix.

Multiply each element of the matrix $\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right]$by 4.

$\begin{array}{c}4C=4\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right]\\ =\left[\begin{array}{cc}4\left(0\right)& 4\left(4\right)\\ 4\left(-2\right)& 4\left(5\right)\\ 4\left(7\right)& 4\left(-1\right)\end{array}\right]\end{array}$

- Simplify

Further simplify the matrix.

$\begin{array}{c}4C=\left[\begin{array}{cc}4\left(0\right)& 4\left(4\right)\\ 4\left(-2\right)& 4\left(5\right)\\ 4\left(7\right)& 4\left(-1\right)\end{array}\right]\\ =\left[\begin{array}{cc}0& 16\\ -8& 20\\ 28& -4\end{array}\right]\end{array}$