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 $\frac{31}{2}$.
Statement $2$: $A$ system of three homogeneous equations in three variables has a nontrivial solution if the determinant of the coefficient matrix is zero.

• A
  Statement $1$ is false,Statement $2$ is true.
• B
  Statement $1$ is true,Statement $2$ is true,Statement $2$ is a correct explanation for Statement $1$.
• C
  Statement $1$ is true,Statement $2$ is true,Statement $2$ is not a correct explanation for Statement $1$.
• D
  Statement $1$ is true,Statement $2$ is false.