GATE 2014 EE (EE1) – Question 56
$A=\begin{pmatrix}0&1&-1\\-6&-11&6\\-6&-11&5\end{pmatrix}$. Find the absolute value of the ratio of maximum eigenvalue to minimum eigenvalue.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2.9 to 3.1
Explanation
The characteristic polynomial is λ³+6λ²+11λ+6=(λ+1)(λ+2)(λ+3), so the eigenvalues are−1,−2,−3. The official answer compares the largest and smallest eigenvalue magnitudes, giving **3/1=3**. Taken literally as the absolute ratio of algebraic maximum−1to minimum−3, the wording would give1/3; the intended magnitude ordering is therefore essential.