Do you have to use elimination?
Can you see that x1=x2=x3?
I'm supposed to solve this matrix equation by GaussJordan elimination and I find it very difficult to see and carry out the row operations mainly because of the z's. If someone is able to help me I would truly appreciate it.
zx1 + x2 + x3 = 1
x1 + zx2 + x3 = 1
x1 + x2 + zx3 = 1
z has a real value.
The fact that it is "z" rather than a number is just means you have to use algebra rather than arithmetic.
The first thing I would do, to simplify the algebra, is swap the first and third rows:
Then "clear" the first column by subtracting the first row from the second and subtracting z times the first row from the third:
Now divide the second row by z-1 to get
and clear the second row by subtracting the second row from the first and subtracting 1- z times the second row from the third.
You try to finish it.