4 1 0 O 2 Let X1 , X2 , and X3 = . Suppose H = Span {x1, x2, x3}. -5 -4 CT Use the Gram-Schmidt process to find an orthogonal basis for H. You do not need to normalize your vectors, but give exact answers. V1= 4 3 -4 X V2 = 14 42 7 42 231 42According to Gram-Schmidt process K - ( C ) YK = OK - Pooj 1=1 where pooj (OCK is vector projection The normalized vector ek = = 4 3 A = 4 S 0 . 62 IV,= 14 + 1 + 374 142 0- 151 142 = V 42 3 0 - 46 42 = 6-48 4 - 0.62"Vo = 26 2 - pRoj ( x 2 ) = - 0. 67 - 0-17 - 5 - 0.51 0' 67 1. 67 6, 17 - 4- 5 - 1.67 0 . 33 1V21 0 03 - 0+ 88 IN - 0.3 3 73 = X3 - Pooja (2(3 ) - Proj (73 - 2.86 2 - 0. 71 - 4 - 2.14 5 2. 86 2 . 86 2. 71 - 1.86 2. 14es = V 3 - 0 .59 0. 56 - 0.38 044 : onthonormal basis are 0.62 10.33 0.59 0.15 0 03 0. 56 0. 46 - 0.88 - 0.38 is answer -0- 62 - 0.33 0 .44 For finding projection use equation Pool ( x K ) = Vj - x k Vi Eg : Proj ( x3 ) = V. x3 VI = - 30 2 . 85 42 w - . - 0 .714 2. 14 Q- 8 6