Eigenvalue-Eigenvector Pair Verification

00:00 3 marks

Given the matrix \(A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}\) and the vector \(v = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\), determine if \(v\) is an eigenvector of \(A\). If yes, provide the corresponding eigenvalue.

Hint Hint

Hint

Substitute \(A\) and \(v\) into the equation \(Av = \lambda v\) and perform the matrix multiplication to verify if the resulting vector is a scalar multiple of \(v\).

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Yes, \(v\) is an eigenvector of \(A\) with the corresponding eigenvalue \(\lambda = 2\).

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Eigenvalue-Eigenvector Pair Verification

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Eigenvalue-Eigenvector Pair Verification

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