I was wondering if you guys could help me out with this. I honestly have no idea how to solve it, since I've been going through different examples but they all use determinants, which we're not supposed to know yet, so we have to solve it with another method. (Gauss, Gauss-Jordan)
Given the system:
$$x+by+az=1$$
$$ax+by+z=a$$
$$x+aby+z=b$$
Find the values of "a" and "b" so that the system has an unique solution, infinite solutions and no solution.
I turned it into a matrix and tried to solved it, but I got nowhere useful. I got this:
\begin{matrix}
1 & b & a & 1 \\
0 & 1 & {a^2\over(ab-b)} & 0 \\
0 & 0 & a^2+a-1 & 1-b \\
\end{matrix}
I would be happy if you could give me some sort of hint or useful way so I can solve this.
Best Answer
Turning the system into a matrix is a good first approach.
Hint: When a system has a unique solution, what does the echelon form of its augmented matrix look like?
Also, is that supposed to be a z in the third equation and not another x?