Examine the consistency of the system of equations: $x+y+z=1$,$2x+3y+2z=2$,and $ax+ay+2az=4$.

For the system of linear equations
$2x + 4y + 2az = b$
$x + 2y + 3z = 4$
$2x - 5y + 2z = 8$
which of the following is $NOT$ correct?

For the system $x-y+z=4, 2x+y-3z=0, x+y+z=2$,the values of $x, y, z$ respectively are given by

Let the system of linear equations $4x + \lambda y + 2z = 0$,$2x - y + z = 0$,and $\mu x + 2y + 3z = 0$ (where $\lambda, \mu \in R$) have a non-trivial solution. Then which of the following is true?

In solving a system of linear equations $AX=B$ by Cramer's rule,in the usual notation,if $\Delta_1=\left|\begin{array}{ccc}-11 & 1 & -7 \\ -4 & 1 & -2 \\ 5 & 1 & 1\end{array}\right|$ and $\Delta_3=\left|\begin{array}{ccc}4 & 1 & -11 \\ 1 & 1 & -4 \\ 4 & 1 & 5\end{array}\right|$,then $X=$

Consider the system of equations: $ax + by + cz = 2$, $bx + cy + az = 2$, $cx + ay + bz = 2$, where $a, b, c$ are real numbers such that $a + b + c = 0$. Then, the system