GATE 2016 ME (ME3) – Question 36
The number of linearly independent eigenvectors of $A=\begin{bmatrix}2&1&0\\0&2&0\\0&0&3\end{bmatrix}$ is ______.
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Correct answer: 2 to 2
Explanation
The eigenvalues are2 with algebraic multiplicity2 and3 with multiplicity1. For λ=2, solving(A−2I)v=0 forces the second and third components to zero, leaving a one-dimensional eigenspace. For λ=3 there is one further independent eigenvector. Hence the total is **2**, not3: the repeated eigenvalue is defective.