GATE 2021 PI – Question 41
Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice
$A=\begin{pmatrix}8&3\\2&7\end{pmatrix}$ has eigenvalues 5 and 10. For constant α and 2×2 identity I, find eigenvalues of B = A+αI.
- 5,10
- 5+α,10+α
- 5−α,10−α
- 5α,10α
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Show answer and explanation
Correct answer: (B) 5+α,10+α
Explanation
For Av = λv, $(A+\alpha I)v=(\lambda+\alpha)v$. Each eigenvalue is shifted by α, giving **5+α and 10+α, B**.
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