Exercise · ZW-EIGENSPACE-007 · ★★☆ Intermediate
Let \(\begin{pmatrix}1&1&0\\0&1&0\\0&0&2\end{pmatrix}\). What is the dimension of the eigenspace of \(\lambda=1\)?
Choose one option.
Show answer
- B. \(1\)
Explanation
\(A-I\) has rank 2, so the kernel has dimension 1: only \(e_1\). Although 1 is a double root, its eigenspace is a line.
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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