Question

18 points Save Answer 3) Use the Gram-Schmidt process to transform the basis 00€ for the Euclidean space Rº with the standard inner product into an orthogonal basis for R3. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after you submit the test. TT TT Paragraph Arial 3 (12pt) - E-T--

Answer 1

Given that, Vi= [ ;], 12 = [3] = [3] [ i Step 1: let ui=41= Step 2: let 42 = \2- ۱۰ بلا LV2, 41) <ui, u,> As. Lui, Ui>=0²+12+2=2 LV2, 4,>= 1 cost olis+1(1)=1 a. from [ 21 - + [1] =1 h Step : let Uz=\z- L\3, 4,) u <ului) ولا لاوروله <U2, U₂) AS, LU2,427 = 8+ (-²)² + (½)² = 1+ 4 + + 2 = 3/4 <\3, 4,) = 6+3+1=4 {\s, Ua>= 1- 3 + ² = 0 Hence, from ☺ О» [ 3 ] - 4 [i] (11-11-13 26,2*3=1:1. 141 Therefore, orthogonal basis is