If 3x1 + 2x2 + x3 = 0, 2x1 + x2 + 4x3 = 0, x1 + 4x2 + x3 = 0 be a system of equations, then?
- It is only the trivial solution x1 = 0, x2 = 0, x3 = 0
- It is consistent
- Determinant of the matrix of coefficients is zero
- None of these
Explanation
RHS all 0 → homogeneous system
Find det of 3 2 1; 2 1 4; 1 4 1 = -34
det ≠ 0 → only x1=x2=x3=0 works
det = 0 would mean infinite solutions. Here it’s not 0.
Last verified on 05-06-2026
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