Find the value of b for which the following system has a non-trivial solution and find all the solutions in this case
$2x + 6z = 0$ $4x + y + bz = 0$ $y - z = 0$
I put this in a matrix and row reduced and got
$\begin{bmatrix}2 & 0 & 6 \\ 0 & 1 & b-12 \\ 0 & 0 & -b+11\end{bmatrix}$
So this has a non-trivial solution when b = 11.
Now what is the way to find all solutions?
Edit:
Had a 6 instead of a b in the second row, third column of the original matrix.