Eigenvector Identification and Verification

00:00 3 marks

Consider the matrix \(A = \begin{pmatrix} 3 & 1 \\ 0 & 2 \end{pmatrix}\). Given that \(v = \begin{pmatrix} 1 \\ k \end{pmatrix}\) is an eigenvector of \(A\) (with \(v
eq 0\)) corresponding to the eigenvalue \(\lambda\), determine the value of \(k\) and the eigenvalue \(\lambda\) such that \(Av = \lambda v\).

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Hint

Remember that for an eigenvector \(v\) the equation \(Av = \lambda v\) must hold with \(v \neq 0\).

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k = -1, \(\lambda = 2\)

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Eigenvector Identification and Verification

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Eigenvector Identification and Verification

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