Question

Entered Result Messages Answer Preview incorrect You have entered vectors which are not 1-1 orthogonal 0 0 incorrect incorrect At least one of the answers above is NOT correct. 2 of the questions remain unanswered (1 pt) 1210 Let A = 341-2 Find orthonormal bases of the kernel, row space, and image (column space) of A Basis of the kernel Basis of the row space Basis of the image (column space)

Answer 1

A = [1 3 2 4 1 1 0 -2] x elementof N mu (A) = > x_1 + 2x_2 + x_3 = 0 = > x_1 = -2x_2 - x_3 3x_1 + 4x_2 + x_3 - 2x_4 = 0 = > -6x_2 - 3x_3 + 4x_2 + x_3 = 2x_4 = > -2x_2 - 2x_3 = 2x_4 = > x_4 = -x_2 - x_3 X = [-2x_2 - x_3 x_2 x_3 (x_2 + x_3)] Null sp = span {(-2 1 0 -1), (-1 0 1 -1)} By Guass smith theorem, basis = {1/squareroot 6 (-2 1 0 -1), squareroot 2/3 (0 -1/2 1 -1/2)} Orthogonal basis = {(-2 1 0 -1), (0 -1/2 1 -1/2)} Row Spam: u_1 = [1 2 1 0], u_2 = v_2 - u_1 middot v_2/u_1 middot u_1 u_1 where v_2 = [3 4 1 -2] = [1 0 -1 -2] Orthogonal basis for Row sp = {(1 2 1 0), (1 0 -1 -2)} = {u_1, u_2}