Consider the system of linear equations in `x , ya n dz :` `""(sin3theta)x-y+z=0` , `(cos2theta)x+4y+3z=0`, `2x+7y+7z=0` Which of the following can be the value of `theta` for which the system has a non-trivial solution (A) `npi+(-1)^npi/6,AAn in Z` (B) `npi+(-1)^npi/3,AAn in Z` (C) `npi+(-1)^npi/9,AAn in Z` (D)none of these

Explanation

To solve the system of linear equations given in the question, we need to find the values of \( \theta \) for which the system has a non-trivial solution. A system of linear equations has a non-trivial solution if the determinant of the coefficient matrix is equal to zero.

Let's denote the equations as follows:

1. \( (\sin 3\theta)x - y + z = 0 \) (Equation 1)
2. \( (\cos 2\theta)x + 4y + 3z = 0 \) (Equation 2)
3. \( 2x + 7y + 7z = 0 \) (Equation 3)

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