Standard +0.3 This is a straightforward Further Maths question requiring students to find an invariant line by solving (A - λI)v = 0 for eigenvalues and eigenvectors, or by using the direct method y = mx where the line maps to itself. While it's a Further Maths topic, the matrix is simple (triangular with obvious eigenvalues 2 and -1), making it easier than average even for Further Pure content.
Find the invariant line of the transformation of the \(x\)-\(y\) plane represented by the matrix \(\begin{pmatrix} 2 & 0 \\ 4 & -1 \end{pmatrix}\). [4]
Find the invariant line of the transformation of the $x$-$y$ plane represented by the matrix $\begin{pmatrix} 2 & 0 \\ 4 & -1 \end{pmatrix}$. [4]
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2018 Q6 [4]}}