GATE 2015 CS (CS3) – Question 23

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

For $M=\begin{pmatrix}1&-1&2\\0&1&0\\1&2&1\end{pmatrix}$, which vectors are eigenvectors for eigenvalue 1? α is any nonzero real number.

Show answer and explanation

Correct answer: (B) α(−4,2,1)

Explanation

Solve (M−I)v=0. The first row gives −v₂+2v₃=0, so v₂=2v₃. The third gives v₁+2v₂=0, so v₁=−4v₃. Every nonzero solution is therefore α(−4,2,1), B.

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