a and b are vectors such that a=(} 4 -1 ) Find b as a column vector. Optional working 2a-3b=(} 17 -5 )

## Step1:<br />Given vectors \(\mathbf{a}\) and \(\mathbf{b}\), with \(\mathbf{a}\) as \(\begin{pmatrix}4\\-1\end{pmatrix}\), and an equality \(2\mathbf{a} - 3\mathbf{b} = \begin{pmatrix}17\\-5\end{pmatrix}\). <br /><br />## Step2:<br />Firstly, multiply the vector \(\mathbf{a}\) by 2. This means every component of \(\mathbf{a}\) is multiplied by 2.<br /><br />### \(2\mathbf{a} =2 \times \begin{pmatrix}4\\-1\end{pmatrix} = \begin{pmatrix}2\times4\\2\times(-1)\end{pmatrix}\)<br /><br />## Step3:<br />Next, you subtract equation \(2\mathbf{a} - 3\mathbf{b}\) established earlier by this new vector \(2\mathbf{a}\). <br /><br />### \(2\mathbf{a} - 3\mathbf{b} - 2\mathbf{a} = \begin{pmatrix}17\\-5\end{pmatrix} - 2\mathbf{a}\)<br /><br />### You rearrange this transaction to give:<br /><br />### \(-3\mathbf{b} = \begin{pmatrix}17\\-5\end{pmatrix} - 2\mathbf{a}\)<br /><br />## Step4:<br />Remember that \(-3\mathbf{b}\) mean each element in \(b\) is multiplied by -3. Accordingly, to find vector \(b\), you divide both sides by -3 to obtain.<br /><br />### \(\mathbf{b} = \frac{1}{-3} \times (\begin{pmatrix}17\\-5\end{pmatrix} - \begin{pmatrix}2\times4\\2\times(-1)\end{pmatrix})\)<br /><br />## Step5:<br />Lastly, perform the subtraction in parentheses and multiplication by the scaler on the right-hand side of the equality. All in once step.