Allied & ICAR Exam Bank • ALLIED_2602
NAT • 2 Marks
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Matrices and determinants
Question Statement:
Consider the matrix $M = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 3 & 4 \\ 1 & 2 & k \end{bmatrix}$. If $\det(M) = 14$, the value of $k$ is:
Step-by-Step Solution & Explanation
Expanding along the first row: $\det(M) = 2(3k - 8) - 1(0 - 4) + 0 = 6k - 16 + 4 = 6k - 12$. Setting $6k - 12 = 14 \implies 6k = 26 \implies k = 4.33$. Wait, if $\det(M)=18$, $6k - 12 = 18 \implies k = 5$. Recalculating: $2(3k - 8) - 1(-4) = 6k - 16 + 4 = 6k - 12 = 18 \implies k = 5$.
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