Question

3 0 2 -1 Find the orthogonal projection of onto 2 1. -2 2 Your answer must be in the form [x1,x2,...,xn).

Answer 1

solution: first we need to know the following formulae . of projected onto then, a. I I ă ă veetor is To Proj and the orthogonal projection, 다. Orth I-proj 5' 3 Here, ă 2 2 2 2 Prod T- 11 a. a. To To 0-2+2-4 - 1 O +1 +1 +4 2 0 11 --- 2 = [0, ſ, - 1-2 "The orthogonal projection is,

Orth a 5 = 5 - Projat 3 11 2 3 + 다. 2 2 -2 کرا 2 = 2 2+ dlm alm slm 2- [3 4 3 8 3 (ans) In the and problem, TO - 3 ă= 11 1 3 - 2 3 b : Prog an يا To ā. 0 -3 -6 +3 - 1+1+4 + 9 2 3 6 2 11 15 - 2 2 3 3 6 [ 2/3 - 2/3, 2/3 CA Ans)