Gaussian elimination involving parameters The problem is :Solve the given system of equations involving the parameter a :
$$x+y+az=1\\
x+ay+z=a\\
ax+y+z=a^2\\
ax+ay+az=a^3 .$$
I tried to solve this using the Gaussian method but I'm stuck because this is $4\times3$ matrix, and the Gaussian process is used for square matrix ? Please help..... 

Subsitute $y=1-x-az$ from the first equation and then $z=  - (a - x + 1)$ from the
second equation, assuming $a\neq 1$. Then the third equation gives $x=(a^2+2a+1)/(a+2)$, the case $a=-2$ being impossible. Then the fourth equation gives
$$
a(a+1)(a-1)=0.
$$
For $a=0$ we have a $3\times 3$ system with unique solution $(x,y,z)=(\frac{1}{2},-\frac{1}{2},\frac{1}{2})$. For $a=1$ we obtain $(x,y,z)=(1-y-z,y,z)$ with two free parameters $x,y$. Otherwise it follows that $a=-1$ and $(x,y,z)=(0,1,0)$.
