24 us=1A2 2/3 lc. Let S span{u2, us}. onto S, i.e. v=p + z where p...
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of w = [1, 2,-1,2]T onto the span of ui-|1,-1, 2, 5]T and u2 [2,1,0,-]. Make sure you are working with an orthonormal basis for u span(u, u2 before you use the usual projection formula.
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of...
Let F = <z, 0, y> and let S be the oriented surface parametrized by G(u, v) = (u2 − v, u, v2) for 0 ≤ u ≤ 6, −1 ≤ v ≤ 4. Calculate the normal component of F to the surface at P = (24, 5, 1) = G(5, 1).
Let V = M2(R), and let U be the span of
S =
2. (a) Let V = M,(R), and let U be the span of s={(1 1) ($ 3). (3), (1 9). (1) 2.)} Find a basis for U contained in S. (b) Let W be the subspace of P spanned by T = {2} + 22 – 1, -2.3 + 2x +1,23 +22² + 2x – 1, 2x3 + x2 +1 -2, 4.23 + 2x2 - -4}. Find...
Problem 6. Let E be the plane: 2xi- x2 x3 = 0, and let P R3R3 be the orthogonal _ projection onto the plane E. Let v 1 (1) What are the image and kernel of P? What is the rank of P? Give a geometric descrip- tion, without relying (2) Give four different vectors e R3 such that Px Pv. (Again, solve geometrically and do not use the matrix of P.) (3) Find Pv (4) Find the reflection of...
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 = 13 2 Also let v= 0 5 3 10 -6 0 11 1 1 7 a) (4 pts) Compute prw(v) where W = Span{u1, U2, U3} CR5. b) [4 pts) Compute prw(v) where w+ denotes the orthogonal complement of W in R5. c) [3 pts) Compute the distance between v and W.
for the question, thanks for your help!
2. Let 2 -2 -11 1 3 S1 8 and b -2 -5 7 A= -4 5 2-9 18 Moreover, let A be the 4 x 3 matrix consisting of columns in S (a) (2.5 pt) Find an orthonormal basis for span(S). Also find the projection of b onto span(S) (b) (1.5 pt) Find the QR-decomposition of A. (c) (1 pt) Find the least square solution & such that |A - bl2 is...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
Find the projection of the vector v onto the subspace S. 0 -1 -1 1 S = span V = 0 0 1 1 projs v = JOLI
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
5. (20 pts. each) Let V -span((1a, -1,0,-4).(-1,1,1,3)). a. Express Vi as a span of basis vectors. b. Let b - (3, 0, 1, -2). Present b as b - p+ z, such that p e V and z e vi