Question

Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 0 1 -1 1 1 0 - 1 3 A= , b= 1 1 5 -1 1 0 7 a. The orthogonal projection of b onto Col A is = (Simplify your answers.) b. A least-squares solution of Ax = b is x= (Simplify your answers.)

Answer 1

A = be - 1 0 3 1 ک 가 а, аз Since the Column a, 92, 93 of A are orthogonal, the orthogonal projection of onto col is given by this formula f = bia, a,na b. a3 a, + + b.ana a. a az ده .43 a = 0 a 22 ааг -1 -1 - 0 b.a, 3 0 +3+5-7 al S 7 a,. a, - O +1+1+1= 3 b.az 3 Z I tots+7= 13 5 1

a.a. O 분 Ito +1+1 = 3 ) t.az 3 -| -1-3 +5 toc I 5 7 زوده -1 I+Itlto: 3 1 Se be - 13 7 - + 3 3 3 - z = O of 13 y to 0 pns + t 5 1 + 13 te 급 A least square solution of Axe 6 is 6 = 19, + 13 at 1 az since i- 3

Now that b is known Solve A2 = 1 But can trivial this is since we already know that weights to place on the columns. of A produce to So 11 ८ -17 13 AX - 1, +5 (3, 4.+1 3 Thank you