1) Let S = {v1, V2, U3, VA, Us, 16, U7} be vectors in RS . Let V denote the span of S and let A denote the 5 x 7 matrix whose ith column is vi for i = 1, . .., 7. Assume that the following matrix E is row equivalent to A. 10010 0 0 0 1 2 10 0 0 E = 0 0 0 0101 0 0 0 0 01 1 00000 0 0 a) Find a basis for V inside S. b) Is v1, v2, v4 a linearly independent set? Find all linear combinations v1, V2, v4 that is equal to the zero vector. c) Find a basis for V inside S that does not contain v1.2) Find a basis for the null space of the matrix 1 2 3 =1 9 Z 2 -2 A=14 4 1 1 2 4 6 =2 (i.e. find a basis for the solution space of the equation Ax = 0). \f4) Let M, denote the vector space of 2 x 2 matrices and W be the set of all 2 x 2 matrices a b A= L n'] such that a + b+ + d = 0. Find a basis for . 5) a) Find all values for A that make the set of vectors v1 and U3 = a linearly dependent set of vectors. b) Let v1, 12, 13 be a linearly independent set of vectors in R3. Let A be a 3 x 3 matrix which is not invertible. Prove or disprove that the set of vectors Avi, Avz, Avg is linearly independent