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Question 250015
JEE Mathematics · Hard

Matrices and Determinants: System of equations MCQ

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System of equationsHardQuestion 250015

Question

For the system AX = 0 to have non-trivial solutions, the condition is:
  1. A
    det(A) = 0
    Correct
  2. B
    det(A) ≠ 0
  3. C
    A = I
  4. D
    rank(A) = n

Correct answer

det(A) = 0

Explanation

The homogeneous system AX = 0 has non-trivial solutions iff A is singular, i.e., det(A) = 0. If det(A) ≠ 0, the only solution is X = 0 (trivial).

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