This problem was confusing me so any help would be greatly appreciated!!

For the case below, find the dimension of V by using an appropriate method to create a basis:

a) V = ([5, 2, 1, 0, -1], [3, 0, 1, 1, 0], [0, 0, 0, 0, 0], [-2, 4, -2, -4, -2], [0, 12, -4, -10, -6], [-6, 0, -2, -2, 0]}), a subset of R^5