Exercise · ZW-EIGENSPACE-002 · ★☆☆ Basic
Let \(A=\operatorname{diag}(2,2,3)\). What is the dimension of the eigenspace of \(\lambda=2\)?
Choose one option.
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- A. \(2\)
Explanation
\(A-2I=\operatorname{diag}(0,0,1)\) has kernel spanned by \(e_1,e_2\): dimension 2.
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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