Question:medium
If the homogeneous system of simultaneous equations \(AX=0\) where \(A = \begin{bmatrix} 9 & 2 & k \\ 1 & -1 & -3 \\ k-1 & 1 & 3 \end{bmatrix}\) has a nontrivial solution, then the possible values of \(k\) are
If the homogeneous system of simultaneous equations \(AX=0\) where \(A = \begin{bmatrix} 9 & 2 & k \\ 1 & -1 & -3 \\ k-1 & 1 & 3 \end{bmatrix}\) has a nontrivial solution, then the possible values of \(k\) are
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For homogeneous systems, "nontrivial solution" is synonymous with \(\det(A) = 0\). Always simplify the inner brackets of the determinant expansion carefully to avoid errors in the resulting quadratic.
Updated On: Jun 24, 2026
- 0,6
- 0,3
- 0,5
- 0,1
- 0,7
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The Correct Option is A
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