Question

1. Use the Gram-Schmidt process to transform the given basis into an orthonormal basis. w= (1, 2, 1,0), w, = (1, 1, 2,0), W3 = (0,1,1, - 2), w4 = (1, 0, 3, 1)

Answer 1

Aala: Given set So W2 W2 {(1,2,2,0) (1,1,2,0) (0,1,1,-2) (1,0,3,1) Wz wy Applying Gram Schmidt Process on s as V, = W, = (1,211,0) 11,112 1+4+1= 6 V₂ = W₂ - <W₂, V,> vi 118, 11² <W, .VI? =((111,2,0)(11211,017 = 1+2+2=5 22-722 +1? this value in putting (1,201,0)=(4360) V₂ = (1,1,2,0) - 5 (1,221,0) 6 3 6 6 36 9 6 2 , ااا > .2 11V, 112 I +9+49'. Il 36 V₂ = Wz - <W 3 ,N₂>Vz 11 V2 11² KW, V27={(0,1,1,-2) (4:37,0) .2 +7 -4+7=1 딜 llV, 112 - > 2 6 6

M Wz, Vin=〈Con,-2) C1,2,1,0)> 2 H 2 3 these values in (2) putting 3 2 = - 병용 일유 13 이 ~ (2) -20) (유) 회 2 2 1vs11 (위 2 + (주) (2) ५ 18 11 36 12) 오 t + 오t 12리 12 1 Vu= Wy-MUZ" -4412312 - CyV2 V3 IV. ||V₂ 11² c) 시Wu, Vi= <C1,0,3,101,2,1, 00〉 l t3 = 9 <0ui2=10,3, 1) 크 6 그 리 ) 3 + 22 - ] c 22, 6 6 3 6 2. Air 10 > 2 +6 -2. 2 -2 . =

이 3 시 ร 3 300+ 1162 212 생 고, 그 고 12. / 2 putting these values in 3 Vu = C1101 311) - 니 (1,211, 0) - 1 x (4) 3 1 text- A (2) ( 1 0 3,1)- (1, 2,10)-2 공이 회금 1) () ($(+ (3) LL 3 3t 노 ㅗ 16 48 48 18 12 so otthonormal basis corses V2 Vul Ill) 121) (Val) Vill 56,56.56 ) ( G 86, V6, 33 3. J33 J33 -13 53,트,353 86 which is required answer. MA T a ponding to s is in s =S 0 V3. / 6 6 { 99 22 7. 99 C 2 13