Reduced echelon form where all variables seem to = 0

[Darkmisc]

Homework Statement

Suppose I have the augmented matrix

0 -1 0 | 0
0 -6 3 | 0
0 -1 0 | 0

Homework Equations

which equates to -y = 0 and -6y + 3z = 0.

The Attempt at a Solution

Would the solution be that x, y and z all equal 0?

Or do I need to let the missing variable, x = s and free variable z = t, so the solution is

1 0
s[ 0 ] + t [ 0.5 ]
0 1

(even though I know y = 0 and therefore the free variable must(?) be 0 ) ?




Thanks.

 

[Dick]

Sort of. Yes, definitely y=0 and z=0. And x is free. z isn't.