Given a set of vectors S = {V1, . .., Vn} consider the coordinate linear map T : R" -> V given by T(x1 , . . . , In) = XIV1+ x2V2t .. + an Vn. 1. What statement about T' corresponds to the statement V = Span {v1, . . ., Vn}? 2. What statement about T' corresponds to the statement { V1, . . ., Vn} is linearly independent?Suppose that W1 and W2 are subspaces of a finite dimensional vector space V. Prove: If dim(W1) + dim(W2) > dim(V) then there is a non-zero vector v E Win W2