Question

Find a basis for the subspace W of R4, spanned by the set of vectors V1 {[1 1 0 -1]}, V2 {[0 1 2 1]}, V3 {[1 0 1 -1]}, V4 {[1 1-6 -3]}
and V5 {[-1 -5 1 0]}

What is the dimension of W?
Let W be the subspace of P3 spanned by:
{t^3 + t^2 -2t +1 , t^2 + 1 , t^3 - 2t , 2t^3 +3t^2 -4t +3}.
Find a basis for W. What is the dimension of w?