0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5 0.5 0.5 -1 -2 (a) Solve the least squares problem Ax = b where b - -2 0 (b) Find the projection matrix P that projects vectors in R4 onto R(A) P = (c) Compute Ax and Pb Pb = 0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5...
(1 point) Let A 0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 0.5 Note that the columns of A are orthonormal (why?). 3 2 (a) Solve the least squares problem Ax b where b 3 <X = (b) Find the projection matrix P that projects vectors in R* onto R(A) P (c) Compute Aî and Pb A Pb
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
(1 point) All vectors are in R". Check the true statements below: A. Not every orthogonal set in R™ is a linearly independent set. B. If a set S= {ui,...,Up} has the property that uiU;=0 whenever i+j, then S is an orthonormal set. C. If the columns of an m x n matrix A are orthonormal, then the linear mapping 1 → Ax preserves lengths. D. The orthogonal projection of y onto v is the same as the orthogonal projection...
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
(1 point) Let 0.5 0.5 0.5 0.5 Ūi = 0.5 0.5 Ū2 = ū3 -0.5 0.5 2 2 -0.5 -0.5 0.5 -0.5 Find a vector ū4 in R4 such that the vectors ū1, 72, 73, and ū4 are orthonormal. 04
T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR factorization of the matrix A is given by: 1-3] [21] [ 11 = [2 1 112] 2 -V2 ماده و V2 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. 5/3 -3
Use the Gram-Schmidt process to find an or- thonormal basis for the subspace of R4 spanned by Xi = (4, 2, 2, 1)", X2 (2,0, 0, 2)", X3 = (1,1, -1, 1). Let A = (x1 X2 X3) and b = (1, 2, 3,1)7. Factor A into a product QR, where Q has an orthonormal set of column vectors and R is up- per triangular. Solve the least squares problem Ax = b.
please answer all the parts step by step 7 t o 17 1.1. Find orthonormal basis of A= 0- 2 0 eigenrectors and eigenvalues, L1 0-1 1.2. Write A in the form A=U DU", where U is orthogonal matrix, Dis diagonal matrix 1.3. solve the problem u + Au=o, uco) = (1,0,00 1.4. Find orthonomal bases for R(A), R (AT), N(A), NIAT). 1.5. Is the system Ax=6, 6 = (1,1,17 consistent? 1.6. Find orthogonal projection of rector 6 outo |...