Question

8. (a) Use the Gram-Schmidt procedure to produce an orthonormal basis for the sub space spanned by W = Do not change the order of the vectors. (b) Express the vector x = as a linear combination of the orthonormal basis obtained in part (a).

Answer 1

Subspau spanned be iefd we'll see of the given set for that consider to L I. A= 10 i then detra) = -11+1)+(2+1) to is ginem vectors are l-I Now let v = (8) = 1!) v =] An orthononnal besis for given subspace is The set { w in the where 24, 2, 4, are given by 4 =V uzu - von 2 } zu - 9024 hou ? Mw V2 240 = 0.1 + (-1) + E) 2 = -3 0.0 + II + EDH) = 2 rol 11 :: a = 61-62] C mw y.14 = 0.3 + 0+ EU (12 = -1 V. U₂ = 3.1 +0. 2 + 1 2 = % CS Scanned with 70% = 1+44 + =1444 = 4 CamScanner .

ott-Ho ~ 23 x16 , 7 L 5 300 mg) ja 30% 35 i osthonoul basis is Scanned with | CamScanner

0 - - 1) = () +(8.740 fe [1] This is achieved by finding & Ar such that Jag P + r = -1 - 0 Tz + < Tapeter = 0 - 0 - + HP-mer = 2 - Adding 0 and 7 Poß 3 / r = tr=2 - SB + 4 x = -1 dm @ fz ß-1=-1 =B=0 to (**)=2 5) - +1 = ? = 1 (=-12) Scanned with CamScanner
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