Question

(1 point) 1 -2 -2 4 -4 -3 0 4 -4 Let y = Vi = V2 = 3 1 0 Compute the distance d from y to the subspace of R* spanned by Vị and V2 . d =

Answer 1

Compute the distance d from y to the subspałe of R4 Pb - 2 Let y -2 -3 -4 V= VE -4 4 3 0 Spanned by vo and Y₂ Solh:- Since Voove (-2)*(-2) + (-4)X(-3) + 4x-4) +1X0 = 0 we conclude that { " ,V,} is an orthogonal set. Now let W = span { vo Va} By the orthogonal de composition theorem: projection of y Projny yov V2 V₂ in W you 0 Vovi here Yo V, = (09X(-2) +(4)X(-4)+0x (4) +(3)X(1) = -15 Vovi (-2)2+(-4)2+(4)? Hu? = 37 -14 yo ve = (UX (-2) +(4)X (-3) + 0x (41+3X60) Yo vz = (−2)2+(-3)2 +(-4)2 + (0)2 29 Now put above xalues. in eqh 2 ĝ = -15 2 - 4 14 위성 37 4 29 -4 28 30 37 1.77633 ale na 29 3-069 897 60 - 42 29 0.309413 -56 29 37 -15 37 -0.405405

co subspace w is 9 the closest point to vector the distance from y to w distance between ů defined to be the y and So -0.77633 y - ģ y 0.930103 -0.309413 3.405405 How distance from y to w is d = 11 y-ġll = (-0.7763372+60.930103)2 +1-0-3094372 + +(3.4054051 d = 3.4.5758918 Answer