GATE 2017 CS (CS2) – Question 62
A real 3×3 matrix has characteristic polynomial $\lambda^3-4\lambda^2+a\lambda+30$ and one eigenvalue 2. Find the largest absolute eigenvalue.
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Correct answer: 5.0 to 5.0
Explanation
Substitute λ=2: 8−16+2a+30=0, giving a=−11. Factor the polynomial as $(\lambda-2)(\lambda^2-2\lambda-15)=(\lambda-2)(\lambda-5)(\lambda+3)$. Eigenvalues are 2,5,−3 and the largest absolute value is 5.