Question 6 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core AS (Further Pure Core AS)
Year	2023
Session	June
Topic	Invariant lines and eigenvalues and vectors

6 The matrix \(\mathbf { M }\) is \(\left( \begin{array} { r r } 2 & 1
- 1 & 0 \end{array} \right)\).

Calculate \(\mathbf { M } ^ { 2 } , \mathbf { M } ^ { 3 }\) and \(\mathbf { M } ^ { 4 }\).
Hence make a conjecture about the matrix \(\mathbf { M } ^ { n }\).
Prove your conjecture.