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 non trivial solution if the determinant of the coefficient matrix is zero.
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 non trivial solution if the determinant of the coefficient matrix is zero.
- [AIEEE 2012]
- 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
Similar Questions
If the system of equation $2 x+\lambda y+3 z=5$, $3 x+2 y-z=7$, $4 x+5 y+\mu z=9$ has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :
- [JEE MAIN 2025]
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right| = $
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right| = $
Let $m$ and $M$ be respectively the minimum and maximum values of
$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$.
Then the ordered pair $( m , M )$ is equal to
Let $m$ and $M$ be respectively the minimum and maximum values of
$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$.
Then the ordered pair $( m , M )$ is equal to
- [JEE MAIN 2020]
The value of $a$ for which the system of equations
$a^3x + ( a + 1)^3y + (a + 2)^3z = 0$ ; $ax + (a + 1) y + ( a + 2) z = 0$ ; $x + y + z = 0$, has a non zero solution is
The value of $a$ for which the system of equations
$a^3x + ( a + 1)^3y + (a + 2)^3z = 0$ ; $ax + (a + 1) y + ( a + 2) z = 0$ ; $x + y + z = 0$, has a non zero solution is
If the system of equation $2x + 3y =\, -1; 3x + y = 2; \lambda x + 2y = \mu $ is consistent, then
If the system of equation $2x + 3y =\, -1; 3x + y = 2; \lambda x + 2y = \mu $ is consistent, then