The system of linear equations $\lambda x + y + z = 3$, $x - y - 2z = 6$, and $-x + y + z = \mu$ has:

The system of linear equations $x + y + z = 2$,$2x + y - z = 3$,and $3x + 2y + kz = 4$ has a unique solution if

The system of equations $x+y+z=5, x+2y+az=9, x+2y+z=b$ is inconsistent if

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

The values of $\lambda$ and $\mu$ for which the system of linear equations $x+y+z=2$,$x+2y+3z=5$,and $x+3y+\lambda z=\mu$ has infinitely many solutions are,respectively:

For a matrix $A=\begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$, if $U_{1}, U_{2}$, and $U_{3}$ are $3 \times 1$ column matrices satisfying $A U_{1}=\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$, $A U_{2}=\begin{bmatrix} 2 \\ 3 \\ 0 \end{bmatrix}$, $A U_{3}=\begin{bmatrix} 2 \\ 3 \\ 1 \end{bmatrix}$, and $U$ is a $3 \times 3$ matrix whose columns are $U_{1}, U_{2}$, and $U_{3}$, then the sum of the elements of $U^{-1}$ is: