Class 12Mathematics3 and 4 .Determinants and MatricesSolution of the Linear equations using Matrices
EasyIf $\begin{bmatrix} 2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}$, then $\begin{bmatrix} x \\ y \\ z \end{bmatrix} =$
- A$\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} + K \begin{bmatrix} 3 \\ 1 \\ -2 \end{bmatrix}, K \in R$
- B$\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} + K \begin{bmatrix} 1 \\ -2 \\ 3 \end{bmatrix}, K \in R$
- C$\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} + K \begin{bmatrix} -2 \\ 1 \\ 3 \end{bmatrix}, K \in R$
- D$\begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} + K \begin{bmatrix} -2 \\ 1 \\ 3 \end{bmatrix}, K \in R$
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Consider the following system of equations: $\alpha x + 2y + z = 1$; $2\alpha x + 3y + z = 1$; $3x + \alpha y + 2z = \beta$. For some $\alpha, \beta \in \mathbb{R}$. Which of the following is $NOT$ correct?
DifficultJEE MAIN 2023
View SolutionLet $a, \lambda, \mu \in \mathbb{R}$. Consider the system of linear equations:
$a x + 2 y = \lambda$
$3 x - 2 y = \mu$
Which of the following statement$(s)$ is(are) correct?
$(A)$ If $a = -3$,then the system has infinitely many solutions for all values of $\lambda$ and $\mu$.
$(B)$ If $a \neq -3$,then the system has a unique solution for all values of $\lambda$ and $\mu$.
$(C)$ If $\lambda + \mu = 0$,then the system has infinitely many solutions for $a = -3$.
$(D)$ If $\lambda + \mu \neq 0$,then the system has no solution for $a = -3$.
$a x + 2 y = \lambda$
$3 x - 2 y = \mu$
Which of the following statement$(s)$ is(are) correct?
$(A)$ If $a = -3$,then the system has infinitely many solutions for all values of $\lambda$ and $\mu$.
$(B)$ If $a \neq -3$,then the system has a unique solution for all values of $\lambda$ and $\mu$.
$(C)$ If $\lambda + \mu = 0$,then the system has infinitely many solutions for $a = -3$.
$(D)$ If $\lambda + \mu \neq 0$,then the system has no solution for $a = -3$.
Let $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 0 & 5 \\ 0 & 2 & 1 \end{bmatrix}$ and $b = \begin{bmatrix} 0 \\ -3 \\ 1 \end{bmatrix}$. Which of the following is true?
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