JEE Main 2012 Mathematics question

Statement 1: If the system of equations x + ky + 3z = 0, 3x + ky − 2z = 0, 2x + 3y − 4z = 0 has a nontrivial solution, then the value of k is . Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.

• (1)Statement 1 is false, Statement 2 is true.Correct
• (2)Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
• (3)Statement 1 is true, Statement 2 is true,, Statement 2 is not a correct explanation for Statement 1.
• (4)Statement 1 is true, Statement 2 is false.