Statement 1: If the system of equations x+k y+3 z=0,3 x+k y-2 z=0,2 x+3 y-4 z=0 has a nontrivial solution, then the value of k is 31 2 . 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.

Step-by-step solution

Given system of equations is aligned & x+k y+3 z=0 & 3 x+k y-2 z=0 & 2 x+3 y-4 z=0 aligned Since, system has non-trivial solution aligned & | array ccc 1 & k & 3 3 & k & -2 2 & 3 & -4 array |=0 & 1(-4 k+6)-k(-12+4)+3(9-2 k)=0 & 4 k+33-6 k=0 k= 33 2 aligned Hence, statement - 1 is false. Statement- 2 is the property. It is a true statement.