An ordered pair $(\alpha , \beta )$ for which the system of linear equations
$\left( {1 + \alpha } \right)x + \beta y + z = 2$ ; $\alpha x + \left( {1 + \beta } \right)y + z = 3$ ; $\alpha x + \beta y + 2z = 2$ has a unique solution, is
An ordered pair $(\alpha , \beta )$ for which the system of linear equations
$\left( {1 + \alpha } \right)x + \beta y + z = 2$ ; $\alpha x + \left( {1 + \beta } \right)y + z = 3$ ; $\alpha x + \beta y + 2z = 2$ has a unique solution, is
- [JEE MAIN 2019]
- A
$(2, 4)$
- B
$(-3, 1)$
- C
$(-4, 2)$
- D
$(1, -3)$
Similar Questions
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]
The value of the determinant $\left| {\begin{array}{*{20}{c}}{{a^2}}&a&1\\{\cos \,(nx)}&{\cos \,(n\, + \,1)\,x}&{\cos \,(n\, + \,2)\,x}\\{\sin \,(nx)}&{\sin \,(n\, + \,1)\,x}&{\sin \,(n\, + \,2)\,x}\end{array}} \right|$ is independent of :
Let $\mathrm{A}$ be a square matrix of order $3 \times 3$ , then $|\mathrm{k A}|$ is equal to
Let $\mathrm{A}$ be a square matrix of order $3 \times 3$ , then $|\mathrm{k A}|$ is equal to
Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(-2,0),(0,4),(0, \mathrm{k})$
Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(-2,0),(0,4),(0, \mathrm{k})$
If $\left| {\,\begin{array}{*{20}{c}}a&b&0\\0&a&b\\b&0&a\end{array}\,} \right| = 0$, then
If $\left| {\,\begin{array}{*{20}{c}}a&b&0\\0&a&b\\b&0&a\end{array}\,} \right| = 0$, then