For the equations $x+2y+3z=1$,$2x+y+3z=2$,and $5x+5y+9z=4$,which of the following is true?

If the system of linear equations $x + ay + z = 3$,$x + 2y + 2z = 6$,and $x + 5y + 3z = b$ has no solution,then:

The bookshop of a particular school has $10$ dozen chemistry books,$8$ dozen physics books,and $10$ dozen economics books. Their selling prices are Rs. $80$,Rs. $60$,and Rs. $40$ each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

If $p$ and $q$ are two distinct real values of $\lambda$ for which the system of equations $\begin{aligned} (\lambda-1) x+(3 \lambda+1) y+2 \lambda z &=0 \\ (\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z &=0 \\ 2 x+(3 \lambda+1) y+3(\lambda-1) z &=0 \end{aligned}$ has a non-zero solution, then $p^2+q^2-p q=$

If the system of linear equations $x - 2y + kz = 1$,$2x + y + z = 2$,and $3x - y - kz = 3$ has a non-zero solution $(x, y, z) \neq 0$,then $(x, y)$ lies on the straight line whose equation is

If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right] A \left[\begin{array}{l} 1 \\ 1 \end{array}\right] = \left[\begin{array}{l} 1 \\ 0 \end{array}\right]$,then $A$ is equal to