Question

nsistent system 0 8 points) Ib) What is the projection of1 ? Please write your answer as a matrix times a vector, without simplifying the result (2 points)

Answer 1

Let A = [1 2 1 -1 0 -1 0 -2] X = [X_1 X_2] B = [1 2 -1 0] Ax = B A^tax = a^t b [1 0 2 -1 1 0 -1 -2][1 2 1 -1 0 -1 0 -2][X_1 X_2] = [1 0 2 -1 1 0 -1 -2][1 2 -1 0] [7 0 0 5][X_1 X_2] = [4 -2] 7X_1 = 4 X_1 = 4/7 5X_2 = -2 X_2 = -2/5 SOLUTION X_1 = 4/7 AND X_2 = -2/5 \R\N projection of vector x = [1 2 -1 0] onto span v = {[1 2 1 -1][0 -1 0 -2]} Let A = [1 2 1 -1 0 -1 0 -2] Projec_v vector x = A(A^TA)^-1 A^T vector x A^TA = [1 0 2 -1 1 0 -1 -2][1 2 1 -1 0 -1 0 -2] = [7 0 0 5] (A^T A)^-1 = 1/35[5 0 0 7] Project_v vector x = 1/35[1 2 1 -1 0 -1 0 -2][5 0 0 7][1 0 2 -1 1 0 -1 -2][1