Determine whether the set of matrices 3 0 3 60 2 3 10 2 2 02

Determine whether the set of matrices {[3 0 -3 6],[0 2 3 1],[0 -2 -2 0],[-2 1 2 1]} is linear independent or linearly dependent in M_22.

Solution

determine whether the set of matrix is linearly independent or linearly dependent in M₂₂

I have the set of matrices:

[3366],[0110],[01284],[1102][3636],[0110],[08124],[1012]

I found the set to be linearly independent by reducing it to row echelon form and having only trivial solutions. (I left out the augmented 0 row)

1000210008101/321/21[1201/301820011/20001]

But this seems to be to also be a spanning set, because if I continue to reduce the matrix to reduced row echelon form I will get a = b = c = d = 0 since there are no non-trivial solutions the set can only be a linear combination of scalars = 0. aM1+bM2+cM3+dM4=0aM1+bM2+cM3+dM4=0.