Allied & ICAR Exam Bank • ALLIED_2626 NAT • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If $A = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$, the spectral radius $\rho(A) = \max |\lambda_i|$ is:

Answer Key:

1

Step-by-Step Solution & Explanation

$\lambda^2 + 1 = 0 \implies \lambda = \pm i$. The magnitude is $|\pm i| = 1$. Hence spectral radius is $1$.
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