Find the best approximation to z by vectors of the form C7 V + c2V2. 3...
#7 6.3.13 Find the best approximation to z by vectors of the form C1V4 +C2V2 2 3 1 -6 - 1 2 za VE V2 3 -3 0 2 1 1 The best approximation to z is (Simplify your answer.)
Find the best approximation to z by vectors of the form CV + C2V2 4 The best approximation to zis (Simplify your answer.)
(1 point) Are the following statements true or false? ? 1. The best approximation to y by elements of a subspace W is given by the vector y - projw(y). ? 2. If W is a subspace of R" and if V is in both W and Wt, then v must be the zero vector. ? 3. If y = Z1 + Z2 , where z is in a subspace W and Z2 is in W+, then Z, must be...
#11 6.3.19 A Question Help 0 Let uy = 2 -2, and uz = 0 . Note that u, and uz are orthogonal but that uz is not orthogonal to u, oruz. It can be shown that uz is not in the subspace 2 W spanned by U, and up. Use this fact to construct a nonzero vector v in R3 that is orthogonal tou, and uz. A nonzero vector in R3 that is orthogonal tou, and uz is v=
Wite **the sum of two vectons, one in Span {u) and one in Span (wa). Assume that (.....) is an orthogonal besis Type an integer or simplified traction for each max element) Verity that {.uz) is an orthogonal sot, and then find the orthogonal projection of y onto Span(uz) y To verty that (0-uz) as an orthogonal set, find u, uz 2-0 (Simplify your answer.) The projection of yonte Span (0,2) 0 (Simplify your answers.) LetW be the subspace spanned...
#12 6.3.20 s Question Help 5 0 Let un 2. u2 -8 and uz = 1 Note that u, and uz are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to - 1 0 construct a nonzero vector v in R3 that is orthogonal to u, and up. 4 The nonzero vector v = is orthogonal to u, and u2
All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer. Complete parts (a) through (e) below. a. If W is a subspace of R" and if y is in both W and wt, then y must be the zero vector. If v is in W, then projwv = Since the wt component of v is equal to v the w+ component of v must be A similar argument can be formed for the W...
3 1 Lety 1 1 V and V2 Find the distance from y to the subspace W of R* spanned by V, and V. given that the closest point to y in W - 2 -1 2 0 13 الميا - 1 -5 is y 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed)
- 4 -1 -2 1 Let y = V1 = and V2 Find the distance from y to the subspace W of R4 spanned by V, and V2, given that the closest 1 -1 0 13 3 -1 -5 point to y in W is y= نيا 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.)
#5 6.3.8 Let W be the subspace spanned by U, and up. Write y as the sum of a vector in W and a vector orthogonal to W. -1 -2 y = un = 3 2 -1 The sum is y = y +z, where y 8. is in W and z = Doo is orthogonal to W. (Simplify your answers.)