(4) Let L be a line in R3 and let T = proL be the projection onto L. what are the eigenvectors of T? Is T diagonalizabl...
Let u= -3 2 4 ; and let L denote the line thru the origin of R3 in the direction of u. The projection of R3 onto L — denoted PL : R3 −→ R3 — is definded to be equal to the projection pu onto the vector u. You may assume that PL is a linear transformation. Find the standard matrix [PL] for PL.
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...
show all work please, thanks Find the projection of vector v onto line L. v = <5,-1,2>, L: x=3, y + 4 22 3 # 1 , 2: Find the projection of vector 1. =(5,-1,2), l: x = onto line f. y+4 3, -1 Z-2 3 y + 4 22 3 # 1 , 2: Find the projection of vector 1. =(5,-1,2), l: x = onto line f. y+4 3, -1 Z-2 3
- Find the projection of a=(−2,1,4) onto the line x=(3,3,−1)+t(1,2,−2) - Find the projection vector of a onto the line given in part a).
What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p of the vector b-5 onto this subspace? Pi P2 Ps What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p...
Let T: R3 → R3 be the linear transformation that projects u onto v = (9, -1, 1). (a) Find the rank and nullity of T. rank nullity (b) Find a basis for the kernel of T.
(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].
-7 (1 point) Compute the orthogonal projection of v = v-3 onto the line L through 4 and the origin. -4 proj( ) =
19 -4 (1 point) Find the orthogonal projection of v17 onto the subspace V of R3 spanned by 4 and-6 7 4 533/51 projv(V)-1267/51 -448/51
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p? 4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...