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...
L2 pt) Let P be the projection matrix that projects vectors onto C(A). Show that (I- P)2 projects vectors onto N(AT). L2 pt) Let P be the projection matrix that projects vectors onto C(A). Show that (I- P)2 projects vectors onto N(AT).
L2 pt) Let P be the projection matrix that projects vectors onto C(A). Show that (I- P)2 projects vectors onto N(AT). L2 pt) Let P be the projection matrix that projects vectors onto C(A). Show that (I- P)2 projects vectors onto N(AT).
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...
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
- 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).
(20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b (c) Find the solutionx to the least square problem for Ax = b. (d) What is the vector in W that best approximates b? (20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b...
(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 diagonalizable? (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 diagonalizable?
Verify that is an orthogonal set, and the find the orthogonal projection of 3 onto Span1 Verify that is an orthogonal set, and the find the orthogonal projection of 3 onto Span1
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...