Note that u, and u are orthogonal. It can be shown that ug is not in...
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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
#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=
Note that and u, are orthogonal it can be shown that t h e wspawned by Use this to constructo r vector in that is orthogonal tow, and u The non vector v s orthogonal tou, and
Find the best approximation to z by vectors of the form C7 V + c2V2. 3 1 3 -1 -6 1 z = V2 4 0 -3 3 1 The best approximation to z is . (Simplify your answer.) - 15 - 8 8 - 1 Let y = , and v2 Find the distance from y to the subspace W of R* spanned by V, and vą, given 1 0 1 - 15 3 3 - 13 09 that...
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. 2 y = 6 un 5 The sum is y=9+z, where y is in W and Z is orthogonal to W. (Simplify your answers.) N
Show that (u, u2 ub) is an orthogonal basis for R Thon express as a inear of the u's Which of the following cniteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of IR? Select all that apply A. The vectors must span W B. The vectors must all have a length of 1 D C. The distance between any pair of distinct vectors must be constant D. The vectors must form...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
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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.)
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...
(1 point) Given v = find the coordinates for v in the subspace W spanned by U = , U2 = 0 and Ug = Note that uy, U, and Uz are orthogonal. v= u+ U2+ 213