Question 5 - A-Level Maths

Exam Board	OCR MEI
Module	Further Extra Pure (Further Extra Pure)
Year	2020
Session	November
Topic	Invariant lines and eigenvalues and vectors

Show that \(\mathbf { f }\) is also an eigenvector of \(\mathbf { A }\).
State the eigenvalue associated with \(\mathbf { f }\). You are now given that \(\mathbf { A }\) represents a reflection in 3-D space.
Explain the significance of \(\mathbf { e }\) and \(\mathbf { f }\) in relation to the transformation that \(\mathbf { A }\) represents.
State the cartesian equation of the plane of reflection of the transformation represented by \(\mathbf { A }\).