Challenging +1.2 This question requires finding invariant lines (eigenvectors) of a 2×2 matrix, which is a standard Further Maths topic. While it involves solving a characteristic equation and working with the condition M(x,y) = λ(x,y), the matrix structure is simple (off-diagonal only) making the algebra straightforward. It's harder than routine A-level questions but represents a standard Further Maths exercise without requiring deep insight.
The \(2 \times 2\) matrix M is defined by
$$\mathbf{M} = \begin{pmatrix} 0 & 0.25 \\ 0.36 & 0 \end{pmatrix}$$
Find, by calculation, the equations of the two lines that pass through the origin, that remain invariant under the transformation represented by M. [4]
The $2 \times 2$ matrix M is defined by
$$\mathbf{M} = \begin{pmatrix} 0 & 0.25 \\ 0.36 & 0 \end{pmatrix}$$
Find, by calculation, the equations of the two lines that pass through the origin, that remain invariant under the transformation represented by M. [4]
\hfill \mbox{\textit{SPS SPS FM 2020 Q10 [4]}}