- A$|a|\, = \,|b|\,.\,|c|\, = 1$
- ✓$b||c$
- C$a||b$
- D$b\, \bot \,c$
i.e., $b||c$ or $a = 0.$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$1.$ The number of matrices in $\Omega$ is
$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$
$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is
$(A)$ less than $4$
$(B)$ at least $4$ but less than $7$
$(C)$ at least $7$ but less than $10$
$(D)$ at least $10$
$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is
$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$