I'm starting linear algebra next week and been trying to get a little ahead. I'm working with a practice sheet I found through Google. One of the problems has the equations
$2x+5y=9$
$x+2y-z=3$
$-3x-4y+7z=1$
I'm putting this system in reduced echelon form, I've tried several different elimination paths but I keep getting the same result which is that the bottom row ends up as
0 0 0 | 4
I can get the system to ref but I'm not sure how to treat this row, all variables have a zero coefficient but there's a non-zero constant.
Do I just ignore that row since it doesn't help me solve the system? Or does it help me solve the system in some way I don't know about yet? Or am I doing my row operations wrong somehow?
I start with the augmented matrix
2 5 0 | 9
1 2 -1 | 3
-3 -4 7 | 1
I do operations
$-R_2+R_1->R_1$
$-R_1+R_2->R_2$
$3R_1+R_3->R_3$
$5R_2+R_3->R_3$
And I end up with the matrix
1 3 1 | 6
0 -1 -2 | -3
0 0 0 | 4
Any help or explanation will be appreciated!
(I'm trying to learn the formatting, thanks for your patience)