Consider the system of equations
$ x-2 y+3 z=-1 $ ; $ -x+y-2 z=k $ ; $ x-3 y+4 z=1$
$STATEMENT -1$ : The system of equations has no solution for $\mathrm{k} \neq 3$. and
$STATEMENT - 2$ : The determinant $\left|\begin{array}{ccc}1 & 3 & -1 \\ -1 & -2 & \mathrm{k} \\ 1 & 4 & 1\end{array}\right| \neq 0$, for $\mathrm{k} \neq 3$.
Consider the system of equations
$ x-2 y+3 z=-1 $ ; $ -x+y-2 z=k $ ; $ x-3 y+4 z=1$
$STATEMENT -1$ : The system of equations has no solution for $\mathrm{k} \neq 3$. and
$STATEMENT - 2$ : The determinant $\left|\begin{array}{ccc}1 & 3 & -1 \\ -1 & -2 & \mathrm{k} \\ 1 & 4 & 1\end{array}\right| \neq 0$, for $\mathrm{k} \neq 3$.
- [IIT 2008]
- A
Statement-$1$ is True, Statement -$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$
- B
Statement -$1$ is True, Statement -$2$ is True; Statement-$2$ is $NOT$ a correct explanation for Statement-$1$
- C
Statement -$1$ is True, Statement -$2$ is False
- D
Statement -$1$ is False, Statement - $2$ is True
Similar Questions
The system of equations $-k x+3 y-14 z=25$ $-15 x+4 y-k z=3$ $-4 x+y+3 z=4$ is consistent for all $k$ in the set
The system of equations $-k x+3 y-14 z=25$ $-15 x+4 y-k z=3$ $-4 x+y+3 z=4$ is consistent for all $k$ in the set
- [JEE MAIN 2022]
$S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x + y + z =1$ ; $x +\lambda y + z =1$ ; $x + y +\lambda z =1$ is inconsistent, then $\sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to
$S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x + y + z =1$ ; $x +\lambda y + z =1$ ; $x + y +\lambda z =1$ is inconsistent, then $\sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to
- [JEE MAIN 2023]
Number of triplets of $a, b \, \& \,c$ for which the system of equations,$ax - by = 2a - b$ and $(c + 1) x + cy = 10 - a + 3 b$ has infinitely many solutions and $x = 1, y = 3$ is one of the solutions, is :
Number of triplets of $a, b \, \& \,c$ for which the system of equations,$ax - by = 2a - b$ and $(c + 1) x + cy = 10 - a + 3 b$ has infinitely many solutions and $x = 1, y = 3$ is one of the solutions, is :
If $x = a + 2b$ satisfies the cubic $(a, b\in R)$ $f (x)=$ $\left| {\,\begin{array}{*{20}{c}}{a - x}&b&b\\b&{a - x}&b\\b&b&{a - x}\end{array}\,} \right|$ $= 0$, then its other two roots are
Consider system of equations $ x + y -az = 1$ ; $2x + ay + z = 1$ ; $ax + y -z = 2$
Consider system of equations $ x + y -az = 1$ ; $2x + ay + z = 1$ ; $ax + y -z = 2$