Exercise · ZW-EIGENSPACE-003 · ★☆☆ Basic
Let \(A=3I\) of size \(2\times 2\). What is the eigenspace of \(\lambda=3\)?
Choose one option.
Show answer
- D. All of \(\mathbb{R}^2\)
Explanation
\(A-3I=0\), whose kernel is all of \(\mathbb{R}^2\): every nonzero vector is an eigenvector.
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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- ZW-EIGENSPACE-005 Which statement about the eigenspace E_λ is true?
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- ZW-EIGENSPACE-007 Let [1 1 0; 0 1 0; 0 0 2]. What is the dimension of the eigenspace of λ=1?
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