Question

Determine the value of h such that the matrix is the augmented matrix of a consistent linear system (matrices)
[ 6 -6 h
-12 12 5]

Answer 1

The system will be inconsistent if you have any rows of the form [0 0 c]
where c is nonzero after you reduce to echelon form, since that row of the matrix would read 0*x1 + 0*x2 = c, which is impossible with real #s.

So go ahead and row reduce, keeping h as a variable as you go, then see what h needs to be to prevent the above row from happening.