1 2 1 3 1. LetA= 2 4 1 2 . 3 6 3 7 (a) Use elementary row operations to get A in Row Echelon Form. (b) Find a basis for the row Space of A, and determine the rank of A. (c) Find a basis for the null Space of A. 1 a: 0 2. Let 2: be a real number and A = 0 1 :1: . w 0 1 (a) Use elementary row Operations to get A in Row Echelon Form. (b) Find all values of a: for which rank(A) = 3, and nd a basis for Row(A) 7 in terms of 3:. (c) Find a value of z for which rank(A) = 2, and for this value of w, nd a basis for Null(A) . 3. Let W be the subSpace of R4 Spanned by the set {(1, 2, 0, 2), (2, 5, 5, 6), (0, 3, 15, 18), (0, 2, 10, 8)} (a) Find a basis for W and the dimension of W. (b) Use the result in (a) to determine whether the following vectors are linearly independent: (1, 2,0, 2), (2, 5, 5, 6), (0, 3,15,18), (0, 2, 10, 8)