Question

let $f=\begin{bmatrix}-1&1&4\\2&5&1end{bmatrix}$ and $g=\begin{bmatrix}6&-7&5\\4&6&-2end{bmatrix}$. find $6f + 4g$. $6f + 4g = \square$

Explanation:

Step1: Calculate \(6F\)

To find \(6F\), we multiply each element of matrix \(F\) by 6.
Given \(F =

$$\begin{bmatrix}-1&1&4\\2&5&1\end{bmatrix}$$

\), then:
\(6F = 6\times

$$\begin{bmatrix}-1&1&4\\2&5&1\end{bmatrix}$$

=

$$\begin{bmatrix}6\times(-1)&6\times1&6\times4\\6\times2&6\times5&6\times1\end{bmatrix}$$

=

$$\begin{bmatrix}-6&6&24\\12&30&6\end{bmatrix}$$

\)

Step2: Calculate \(4G\)

To find \(4G\), we multiply each element of matrix \(G\) by 4.
Given \(G =

$$\begin{bmatrix}6&-7&5\\4&6&-2\end{bmatrix}$$

\), then:
\(4G = 4\times

$$\begin{bmatrix}6&-7&5\\4&6&-2\end{bmatrix}$$

=

$$\begin{bmatrix}4\times6&4\times(-7)&4\times5\\4\times4&4\times6&4\times(-2)\end{bmatrix}$$

=

$$\begin{bmatrix}24&-28&20\\16&24&-8\end{bmatrix}$$

\)

Step3: Add \(6F\) and \(4G\)

To add two matrices, we add their corresponding elements.
\(6F + 4G=

$$\begin{bmatrix}-6 + 24&6+(-28)&24 + 20\\12+16&30 + 24&6+(-8)\end{bmatrix}$$

=

$$\begin{bmatrix}18&-22&44\\28&54&-2\end{bmatrix}$$

\)

Answer:

\(

$$\begin{bmatrix}18&-22&44\\28&54&-2\end{bmatrix}$$

\)