Exercise · ZW-EIGENVALUE-AND-EIGENVECTOR-003 · ★☆☆ Basic

The vectors \((1,0)\) and \((1,-1)\) are eigenvectors of \(A=\begin{pmatrix}3&1\\0&2\end{pmatrix}\). What are their eigenvalues, in that order?

Choose one option.

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  • D. \(3\) and \(2\)

Explanation

\(A(1,0)=(3,0)=3(1,0)\) and \(A(1,-1)=(2,-2)=2(1,-1)\): the eigenvalues are 3 and 2.

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Review the concept: Eigenvalue and eigenvector

An eigenvector \(v\) of a square matrix \(A\) is a nonzero vector that \(A\) only stretches, shrinks or flips, without taking it off its line; the factor \(\lambda\) is its eigenvalue.

\[Av=\lambda v,\quad v\neq 0\]

More practice problems: eigenvalue and eigenvector

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