Exercise · ZW-EIGENSPACE-004 · ★☆☆ Basic
Let \(\begin{pmatrix}2&1\\0&2\end{pmatrix}\). What is the dimension of the eigenspace of \(\lambda=2\)?
Choose one option.
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- B. \(1\)
Explanation
\(A-2I=\begin{pmatrix}0&1\\0&0\end{pmatrix}\) has rank 1, so its kernel has dimension \(2-1=1\).
Review the concept: Eigenspace
The eigenspace \(E_\lambda\) of a square matrix \(A\) for the eigenvalue \(\lambda\) is zero together with the eigenvectors of \(\lambda\), where \(I\) is the identity of the size of \(A\).
\[E_\lambda=\ker(A-\lambda I)\]
More practice problems: eigenspace
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