A2 October 2021 Paper 1 Q6
6 Given that \(y = mx\) is an invariant line of the transformation with matrix \(\begin{pmatrix} 1 & 2 \\ 2 & -2 \end{pmatrix}\), determine the possible values of \(m\). [4]
| Scheme | Marks | AO |
|---|---|---|
| \(\begin{pmatrix} 1 & 2 \\ 2 & -2 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} x + 2y \\ 2x - 2y \end{pmatrix}\) | M1 | 1.1 |
| substituting \(y = mx\) and \(2x - 2y = m(x + 2y)\) | M1 | 2.1 |
| \(2x - 2mx = m(x + 2mx)\) \(\Rightarrow 2m^2 + 3m - 2 = 0\) | A1 | 1.1 |
| \(\Rightarrow m = -2, \frac{1}{2}\) | A1 | 2.2a |
| [4] |
Notes
M1: Could see \(mx\) instead of \(y\) in the initial matrix multiplication for this mark