Quick questions on Diagonalisation explained: H2 Further Mathematics

4short 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 errors in

\mathbf{P}^{-1}

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A slip here propagates through the whole product; verify with

\mathbf{P}\mathbf{P}^{-1} = \mathbf{I}

What is q1?

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State the diagonalisation factorisation and what

\mathbf{P}

and

\mathbf{D}

contain. [2 marks]

What is q2?

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Write

\mathbf{A}^n

in terms of

\mathbf{P}

and

\mathbf{D}

. [1 mark]

What is q3?

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Why does having two distinct eigenvalues guarantee a

2\times2

matrix is diagonalisable? [2 marks]

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