Let S = {v1, v2, V3, V4, V5} be a set of five vectors in 123 Let W = span {S}. When these vectors are placed as columns into a matrix A as A = (v1 V2 V3 V4 V5) and A is row-reduced to echelon form U, we have 1 4 -2 3 2 U = 01 3 1 3 0 0 1 2 1. State the dimension of W = 3 2. State a basis B for W/ using the standard algorithm, using vectors v; with i as small as possible. Express your answer as a set with enclosing braces { and } and use the notation v3 for vg etc. Eg, a typical answer might look like (v1, v3). {v1, v2, v3} OGG 3. Express v as a linear combination of the basis vectors in B. Just write the linear combination with no v= = and use asterisk * for scalar multiplication and v1, v2 etc for vectors in B. Eg, a typical answer might look like 3*v1 - v2 + 2*v4. X