Question

let $b = \

$$\begin{bmatrix}-7 & 6 & 7 \\\\ 3 & 0 & 0\\end{bmatrix}$$

$ (note: there may be a formatting error in the original matrix, assuming the correct $b$ is as per common matrix notation) and $c = \

$$\begin{bmatrix}4 & 1 & 0 \\\\ -5 & 5 & 6\\end{bmatrix}$$

$. find $-2b + 6c$.

Explanation:

Step1: Find -2B

Given \( B =

$$\begin{bmatrix}-7 & 3 \\ 6 & 0 \\ 7 & 0\end{bmatrix}$$

\), multiply each element by -2:
\( -2B =

$$\begin{bmatrix}-2\times(-7) & -2\times3 \\ -2\times6 & -2\times0 \\ -2\times7 & -2\times0\end{bmatrix}$$

=

$$\begin{bmatrix}14 & -6 \\ -12 & 0 \\ -14 & 0\end{bmatrix}$$

\)

Step2: Find 6C

Given \( C =

$$\begin{bmatrix}4 & -5 \\ 1 & 5 \\ 0 & 6\end{bmatrix}$$

\), multiply each element by 6:
\( 6C =

$$\begin{bmatrix}6\times4 & 6\times(-5) \\ 6\times1 & 6\times5 \\ 6\times0 & 6\times6\end{bmatrix}$$

=

$$\begin{bmatrix}24 & -30 \\ 6 & 30 \\ 0 & 36\end{bmatrix}$$

\)

Step3: Add -2B and 6C

Add the corresponding elements of -2B and 6C:
\( -2B + 6C =

$$\begin{bmatrix}14 + 24 & -6 + (-30) \\ -12 + 6 & 0 + 30 \\ -14 + 0 & 0 + 36\end{bmatrix}$$

=

$$\begin{bmatrix}38 & -36 \\ -6 & 30 \\ -14 & 36\end{bmatrix}$$

\)

Answer:

\(

$$\begin{bmatrix}38 & -36 \\ -6 & 30 \\ -14 & 36\end{bmatrix}$$

\)