GATE Civil 2025 Set 2 | Question: 35

Question

Pick the CORRECT eigen value(s) of the matrix $[A]$ from the following choices.
$$[A]=\left[\begin{array}{ll} 6 & 8 \\ 4 & 2 \end{array}\right]$$

• A. $10$
• B. $4$
• C. $-2$
• D. $-10$

Answer 1

a,c

Answer 2

 Important Rule}:

1. Sum of eigenvalues = Trace; 
2. Product of eigenvalues = Determinant.

$\text{Trace} = 6 + 2 = 8$ 
$\text{Determinant} = (6)(2) - (8)(4) = 12 - 32 = -20$

Characteristic equation: $\lambda^2 - 8\lambda - 20 = 0\implies(\lambda - 10)(\lambda + 2) = 0 \implies \lambda = 10, -2$

 $10$ and $-2$ (Options A and C)