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The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0, -x + 4y + 7z = 0, (sin 3θ)x + (cos 2θ)y + 2z = 0 has a non-trivial solution, is -

1. (1) two
2. (2) one
3. (3) four
4. (4) three

Correct answer: (1) two

Solution

The system of equations has a non-trivial solution when the determinant of the coefficient matrix is zero. By analyzing the conditions under which the determinant vanishes, we find that there are two specific values of θ ∈ (0, π) that satisfy this condition.

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