Allied & ICAR Exam Bank • ALLIED_0010 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Solutions of linear equations

Question Statement:

For what value of $k$ does the homogeneous system of equations $x + 2y = 0$ and $3x + k y = 0$ have non-trivial solutions?

Answer Key:

6

Step-by-Step Solution & Explanation

For non-trivial solutions, $\det = 1(k) - 2(3) = 0 \implies k = 6$.
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