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Being W the subspace of R generated by (1,-2,3,-1), (1,1,-2,3) determine a basis and the dimension of the subspace.

Won't the vectors given work as a basis, as long as they are linearly independent?

If so, all we have to do is check for dependance, and if the system is dependent, we would choose one of the vectors as a base, and the dimention would be 1. if it was independent, the basis would be both of those vectors, and the dimention would be 2.

By the same logic, If I was asked to determine the dimention of the subspace generated by those vectors, i'd just check for linear dependance.

Is this right?

By the way, should I simplify the basis by putting them in a matrix and getting it to row-echelon form? would the basis still "work" after that?