Question

624615 400 05 4021 325 1307 05 -14 2185 20.1077 The answer above is NOT correct 5 3 3 -4 10 -21 onto the subspace W spanned by 0 4 (1 point) Find the orthogonal projection of u = 10 -4397/325 406/65 projw (0) -4621/325 1307/65 Preview My Answers Submit Answers Your score was recorded You have attempted this problem 1 time. You received a score of 0% for this attempt Your overall recorded score is 0% You have unlimited attempts remaining

Answer 1

g. Find the -4 10 - 21 orthogonal projetion of subspace w spanned by onto the {#:22-23 To Find: pooj w() = ? solution : let W be a the subspace spanned by u, U2 & Uz. 9 given Vectors the definition, the orthogonal poojection of By ř onto is : W Uzov ut U₂ + Uz poojuca) = ( ) Uzov Uz.uz U₂ U₂ We have: = U₂ Uz=1-1 4,- 3 0 4 2 c -4 V = -21

2 udi = [-5 3 U] 4 (-5)+(g) +(o 4(4) 二 304 - 25 +9 +16 A. = 50 UV = [-5 3 0 41-4 20+30 +0 +40 二 10 -21 lo V = =90 4. Jay = [s。 4 (3) + (6) + (4)+(-5) 1 - 3 4 or (if /s* 3+16+25 四. = 50 5] 4 1. V = [3。 4 川 -12 十D-84-5o - 25 2. V = -146 2 32 4-[-5 -1 (-5)+(-1)+(2)+(2) 二 2 > 25 +1+9+4 99 -39

Uz. V = [-5 -1 3 3 2]-4 2 20-10-63+20 - lo -21 To Uz. V - -33 Thus, 3 -33 pooj w CV) = + + -146 50 ( 39 -1 3 50 2 | 65 39 -9 -438 50 27/5 + + 33 39 -99 39 -66 39 -584 50 730 50 36 5 -4397 325 poojalu) = 406 65 ANSWER NSWER ooo -4621 325 1307 65