For a homogeneous system of equations AX = O, a non-trivial solution exists only if: A. |A| = 0 B. |A| ≠ 0 C. |A| = 1 D. A is an identity matrix Answer: A) |A| = 0 Explanation: If |A| ≠ 0, only the trivial solution (X=O) exists. For non-trivial (non-zero) solutions, |A| must be 0.

imo class 12 determinants

For a homogeneous system of equations AX = O, a non-trivial solution exists only if:

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For a homogeneous system of equations AX = O, a non-trivial solution exists only if:

Answer: A) |A| = 0

Explanation: If |A| ≠ 0, only the trivial solution (X=O) exists. For non-trivial (non-zero) solutions, |A| must be 0.