Answer
$4\mathbf{w}-3\mathbf{v}=5\mathbf{i}-45\mathbf{j}$
Work Step by Step
Here,
$\begin{align}
& {{a}_{1}}=-3 \\
& {{a}_{2}}=-1 \\
& {{b}_{1}}=7 \\
& {{b}_{2}}=-6
\end{align}$
$\begin{align}
& {{k}_{1}}=3 \\
& {{k}_{2}}=4 \\
\end{align}$
Therefore, the value of $3\mathbf{v},4\mathbf{w}$ is,
$\begin{align}
& 3\mathbf{v}=\left[ 3\times \left( -3 \right) \right]\mathbf{i}+\left[ 3\times 7 \right]\mathbf{j} \\
& =-9\mathbf{i}+21\mathbf{j}
\end{align}$
$\begin{align}
& 4\mathbf{w}=\left[ 4\times \left( -1 \right) \right]\mathbf{i}+\left[ 4\times \left( -6 \right) \right]\mathbf{j} \\
& =-4\mathbf{i}-24\mathbf{j}
\end{align}$
Subtract $3\mathbf{v}$ from $4\mathbf{w}$ to get,
$\begin{align}
& 4\mathbf{w}-3\mathbf{v}=\left[ -4-\left( -9 \right) \right]\mathbf{i}+\left[ -24-\left( 21 \right) \right]\mathbf{j} \\
& =5\mathbf{i}-45\mathbf{j}
\end{align}$
