GATE 2023 BM – Question 14
For $A=\begin{pmatrix}1&1&0\\1&-1&0\\1&-1&1\end{pmatrix}$, which vector is an eigenvector corresponding to eigenvalue 1?
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Correct answer: (D) $(0,0,1)^T$
Explanation
Solve (A−I)v=0. The first row gives the second component zero, and the second row then gives the first component zero. The third component is free and must be nonzero for an eigenvector. Thus (0,0,1)ᵀ, D, satisfies Av=v.