Allied & ICAR Exam Bank • ALLIED_0016 NAT • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

For a $2 \times 2$ matrix $A$, if $\text{Trace}(A) = 7$ and $\det(A) = 12$, the smaller eigenvalue is:

Answer Key:

3

Step-by-Step Solution & Explanation

Characteristic equation $\lambda^2 - 7\lambda + 12 = 0 \implies (\lambda - 3)(\lambda - 4) = 0$. The smaller eigenvalue is $3$.
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