Question

determine whether the given vector A in M22 belongs to the span (a1,a2,a3) where a1=[1 -1; 0 3]
a2=[1 1; 0 2]
a3=[2 2; -1 1]

and A=[5 1; -1 9]

so I set up an augmented matrix , but im not sure if I set it up correctly. I made a1 a2 and a3 into columns.

1 1 2 | 5
0 0 -1 | -1
-1 1 2 | 1
3 2 1 | 9

then I did the ref and found that it was inconsistent so I concluded A is not in the span.

is this correct?