Standard +0.3 This is a straightforward application of matrix transformations to find the image of a line. Students need to parametrize the line, apply the matrix transformation, and eliminate the parameter to find the new line equation. It's a standard FP1 technique with clear steps, slightly above average difficulty only because it requires understanding the parametrization method rather than just matrix multiplication.
A transformation \(T: \mathbb{R}^2 \to \mathbb{R}^2\) is represented by the matrix
$$\mathbf{A} = \begin{pmatrix} -4 & 2 \\ 2 & -1 \end{pmatrix}, \text{ where } k \text{ is a constant.}$$
Find the image under \(T\) of the line with equation \(y = 2x + 1\).
[2]
A transformation $T: \mathbb{R}^2 \to \mathbb{R}^2$ is represented by the matrix
$$\mathbf{A} = \begin{pmatrix} -4 & 2 \\ 2 & -1 \end{pmatrix}, \text{ where } k \text{ is a constant.}$$
Find the image under $T$ of the line with equation $y = 2x + 1$.
[2]
\hfill \mbox{\textit{Edexcel FP1 Q31 [2]}}