Class 12Mathematics3 and 4 .Determinants and MatricesSolution of the Linear equations using Matrices
MediumThe following system of linear equations is given: $2x + 3y + 2z = 9$,$3x + 2y + 2z = 9$,and $x - y + 4z = 8$. Which of the following statements is true?
- Ahas a solution $(\alpha, \beta, \gamma)$ satisfying $\alpha + \beta^2 + \gamma^3 = 12$
- Bhas infinitely many solutions
- Cdoes not have any solution
- Dhas a unique solution
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Similar Questions
If the system of equations $x+y+z=2$,$2x+4y-z=6$,and $3x+2y+\lambda z=\mu$ has infinitely many solutions,then:
If the system of equations
$2x + y - z = 5$
$2x - 5y + \lambda z = \mu$
$x + 2y - 5z = 7$
has infinitely many solutions,then $(\lambda + \mu)^2 + (\lambda - \mu)^2$ is equal to
$2x + y - z = 5$
$2x - 5y + \lambda z = \mu$
$x + 2y - 5z = 7$
has infinitely many solutions,then $(\lambda + \mu)^2 + (\lambda - \mu)^2$ is equal to
DifficultJEE MAIN 2023
View SolutionIf $AX=B$,where $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 2 & 1\end{array}\right]$,$X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$,and $B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$,then find the value of $2x+y-z$.
The system of equations $4x + y - 2z = 0$,$x - 2y + z = 0$,and $x + y - z = 0$ has
If the augmented matrix corresponding to the system of equations $x+y-z=1$,$2x+4y-z=0$ and $3x+4y+5z=18$ is transformed to $\left[\begin{array}{cccc}1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32\end{array}\right]$,then $\sqrt{a+b+c}=$
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