Quick questions on Eigenvalues and eigenvectors: the characteristic equation and invariant lines - CCEA A-Level Further Maths

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is q1?

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Write down the characteristic equation for

\begin{pmatrix} 5 & 0 \\ 0 & 2 \end{pmatrix}

. [1 mark]

What is q2?

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An eigenvalue equals

1

. What is special about its invariant line? [1 mark]

What is q3?

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Find an eigenvector of

\begin{pmatrix} 3 & 0 \\ 0 & 7 \end{pmatrix}

for

\lambda = 7

. [1 mark]

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