Question

1 -1 1 6. Find orthonormal b ases for the four fundamental subsp aces of A 2 -2 7. Find the singular value decomposition of A in the above problem.

Answer 1

"A = [1 -2 2 -1 2 -2] To find: Orthogonal basis for A w = {[1 -2 2], [-1 2 -2]} v_1 = [1 -2 2], v_2 = [-1 2 -2] v_1 - v_2 = -1 - 4 - 4 = -9 notequalto 0 These are not orthogonal process w_1 = v_1 w_2 = v_2 + av_1 where a is scales to be determined so that w_1 middot w_2 = 0 0 = v_1(v_2 + av_1) 0 = v_1 middot v_2 + av_1 middot v_1 0 = -9 + 9a a = 1 w_2 = v_2 + v_1 = [-1 2 2] + [1 -2 2] = [0 4] Thus, the set {w_1, w_2} is an orthogonal basis for w However, the length is not 1 as
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