The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has

For $\alpha, \beta \in R$,suppose the system of linear equations $x-y+z=5$,$2x+2y+\alpha z=8$,and $3x-y+4z=\beta$ has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of:

The system of equations $x+3by+bz=0$, $x+2ay+az=0$ and $x+4cy+cz=0$ has

The values of $x, y, z$ in order for the system of equations $3x + y + 2z = 3,$ $2x - 3y - z = -3,$ and $x + 2y + z = 4$ are:

Given the system of linear equations: $2x + 3y + 4z = 9$,$4x + 9y + 3z = 10$,and $5x + 10y + 5z = 11$. The value of $x$ is given by:

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