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Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto...
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let P2 R2 R2 be the orthogonal projection onto the line L2: x32 2r2 0. 0. (1) What are the image and kernel of P2P What is the rank of P2P? Give a geometric description, without relying on the matrix of P2P (2) Find the matrix that represents P2P Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let...
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
(1 point) Find the matrix A of the orthogonal projection onto the line L in R2 that consists of all scalar multiples of the vector [63].
(Section 11.3) Find the projection of u onto v and find the vector component of u orthogonal to v for: u=8 i+2j v = (2, 1, -2)
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p20)- a. Compute the orthogonal projection of p2 onto the subspace spanned by Po and P1 b. Find a polynomial q that is orthogonal to Po and p,, such that Po P is an orthogonal basis for Span(Po P1, P2). Scale the polynomial q so that its vector of values at a2(Simplify your answer.) Let Ps have the inner product given...
Verify that (u,,uz) is an orthogonal set, and then find the orthogonal projection of y onto Span (u.uz). 1-17 [3] 2,,= -1 . uz = = To verify that (uy,uz) is an orthogonal set, find u. U. Uyuz = 0 (Simplify your answer.) The projection of y onto Span{u,, 42} is (Simplify your answers.)
(1 point) Find the orthogonal projection of U = onto the subspace W of R4 spanned by --0-0-1 Uw =
I will upvote! (2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of f(a) – 332 – 1 onto the subspaco V (1 point) Use the inner product < 1.9 > spanned by g(x) - and h(x) - 1 proj) (1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4 -5 X1 = and X2 == 1 -28 -4 0 -32276/5641 -2789775641 projv...
Let P3 have the inner product given by evaluation at -6, -1, 1, and 6. Let po(t) = 1, p1(t) = 2t, and P2 (t) = ? a. Compute the orthogonal projection of P2 onto the subspace spanned by Po and P4. b. Find a polynomial q that is orthogonal to po and p1, such that {PO,P1,93 is an orthogonal basis for Span{PO,P1.P2}. Scale the polynomial q so that its vector of values at ( - 6, - 1,1,6) is...
Verify that {u7,42} is an orthogonal set, and then find the orthogonal projection of y onto Span{uq, 42}- 6 3 - 4 y- . 01 u:- -2 0 To verify that (14,42} is an orthogonal set, find uy • 42. u uy - (Simplify your answer.) The projection of y onto Span{44,42} is .. (Simplify your answers.)