Question

If the equations \( x + ay = 0 \), \( 2x + y + az = 0 \), \( ax + y + 2z = 0 \) have non-trivial solutions, then \( a = \):

• A. 2
• B. -2
• C. \( \sqrt{3} \)
• D. \( -\sqrt{3} \)

Hint:

For a system of linear equations to have non-trivial solutions, the determinant of the coefficient matrix must be zero.

Answer 1

The Correct Option is C

Step 1: To solve for \( a \), calculate the determinant of the coefficient matrix. For non-trivial solutions, the determinant should be zero.
Step 2: After calculating, we find that \( a = \sqrt{3} \).

Final Answer: \[ \boxed{\sqrt{3}} \]