Easy
Let $AX=D$ be a system of three linear non-homogeneous equations. If $|A|=0$ and $\operatorname{rank}(A)=\operatorname{rank}([AD])=\alpha$, then
- A$AX=D$ will have infinite number of solutions when $\alpha=3$
- B$AX=D$ will have unique solution when $\alpha < 3$
- C$AX=D$ will have infinite number of solutions when $\alpha < 3$
- D$AX=D$ will have no solution when $\alpha < 3$
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DifficultJEE MAIN 2022
View SolutionIf the system of equations $\begin{bmatrix} 1 & -2 & 5 \\ 2 & -1 & 1 \\ 11 & -7 & p \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3 \\ 1 \\ q \end{bmatrix}$ has infinitely many solutions,then:
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