Higher June 2022 Paper 3 Q13
13 \(\mathbf{a}\) and \(\mathbf{b}\) are vectors such that
\(\mathbf{a} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\) and \(3\mathbf{a} - 2\mathbf{b} = \begin{pmatrix} 8 \\ -17 \end{pmatrix}\)
Find \(\mathbf{b}\) as a column vector. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) | M1 | for \(3\begin{pmatrix} 2 \\ -3 \end{pmatrix} - 2\mathbf{b} = \begin{pmatrix} 8 \\ -17 \end{pmatrix}\) oe or for \(\begin{pmatrix} 6 \\ -9 \end{pmatrix}\) |
| M1 | for \(2\mathbf{b} = \begin{pmatrix} 3 \times 2 - 8 \\ 3 \times -3 - -17 \end{pmatrix} \left(= \begin{pmatrix} -2 \\ 8 \end{pmatrix}\right)\) oe or \(-2\mathbf{b} = \begin{pmatrix} 8 - 3 \times 2 \\ -17 - 3 \times -3 \end{pmatrix} \left(= \begin{pmatrix} 2 \\ -8 \end{pmatrix}\right)\) oe or for one element correct, \(-1\) or 4 | |
| A1 | cao (if M0 scored, SC B1 for \(\begin{pmatrix} 1 \\ -4 \end{pmatrix}\)) |
Additional guidance
Must see “\(2\mathbf{b} = \ldots\)” or “\(-2\mathbf{b} = \ldots\)” to award 2 marks
One correct element scores 2 marks