(12 marks) (a) (6 marks) Given the matrices A and the reduced echelon form of A below, find: i. a basis for Row(A). What is the dimension of Row(A)? ii. a basis for Col(A). What is the dimension of Col(A)? iii. a basis for Nul(A). What is the dimension of Nul(A)? 1 0 1 23 4 5 10-5/3 A = 10 1 2 -1 2246 4 0 1 1 0 8/3 rref(A) = 00 0 1 1/3 1 1 20 1 0000 0 (b) (2 marks) Consider vectors V = [1,-1, 5, 2], V2 = [-2, 3, 1, 0], V3 = [9, 10, 34, 14], v = [0, 4, 2, 3], v5 = [-3, 31, 41, -8 in R4. Find a basis and the dimension of the subspace W = span{V1, V2, V3, V4, V5}. NOTE: RREF of the matrix whose columns are vectors V1, V2, V3, V4, V5 is 1 0 7 05 0 1 -1 04 0 0 0 1 6 00 000 (c) (4 marks) Let A be an m x n matrix. Prove that every vector in the null space of A is orthogonal to every vector in the row space of A.