Allied & ICAR Exam Bank • ALLIED_2623 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The matrix $A = \begin{bmatrix} 1 & 4 \\ 2 & 3 \end{bmatrix}$ has a positive eigenvalue $\lambda_1$ and a negative eigenvalue $\lambda_2$. The value of $\lambda_1$ is:

Answer Key:

5

Step-by-Step Solution & Explanation

$\det(A - \lambda I) = (1 - \lambda)(3 - \lambda) - 8 = \lambda^2 - 4\lambda - 5 = (\lambda - 5)(\lambda + 1) = 0$. Positive eigenvalue is $5$.
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