The system of equations ${x_1} + 2{x_2} + 3{x_3} = a$,$2{x_1} + 3{x_2} + {x_3} = b$,and $3{x_1} + {x_2} + 2{x_3} = c$ has:

If the system of equations
$2x + y - z = 5$
$2x - 5y + \lambda z = \mu$
$x + 2y - 5z = 7$
has infinitely many solutions,then $(\lambda + \mu)^2 + (\lambda - \mu)^2$ is equal to

Let $[\lambda]$ be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which the system of linear equations $x+y+z=4$,$3x+2y+5z=3$,$9x+4y+(28+[\lambda])z=[\lambda]$ has a solution is:

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix}$,find $A^{-1}$. Using $A^{-1}$,solve the system of equations: $2x - 3y + 5z = 11$,$3x + 2y - 4z = -5$,and $x + y - 2z = -3$.

The values of $\lambda$ and $\mu$ such that the system of equations $x+y+z=6$,$3x+5y+5z=26$,and $x+2y+\lambda z=\mu$ has no solution are:

The system $2x + 3y + z = 5$,$3x + y + 5z = 7$ and $x + 4y - 2z = 3$ has