== 2 1 3 (1 point) Let A 1 and b -3 2 6 The QR...

Question

Question

== 2 1 3 (1 point) Let A 1 and b -3 2 6 The QR factorization of the matrix A is given by: 1 2 = ſ v2 ŠV2 0 V2 3 2 3 (a) Apply

Answer 1

Answer #1

d 3 20 solution: a) 513 √213 213 3 QTb 13 2213 d = 2/3 100-316 where --3 m so 2-1 + 4 - 22 - 252 -12 5 -212-352 Thus, @ 3 Х 5

Please feel free to ask any doubts regarding the solution.

Kind regards.

Answer 2

Similar Homework Help Questions

T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR...

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
2 9 11 and b (1 point) Let A -6 The QR factorization of the matrix...

2 9 11 and b (1 point) Let A -6 The QR factorization of the matrix A is given by: 2 1 6 17 äv2 3 1 1 0 3 2 3 21 V2 3 áva (a) Applying the QR factorization to solving the least squares problem Ax b gives the system: X = 0 2 3 (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. x=
Section 5.6 QR Factorization: Problem 6 Previous Problem Problem List Next Problem 2 9 (1 point)...

Section 5.6 QR Factorization: Problem 6 Previous Problem Problem List Next Problem 2 9 (1 point) Let A = 1 1 and b = 6 The QR factorization of the matrix A is given by: 2 6 1 3 1 1 -ŠV2 V2 *V2 ܝܙܚܐܝ 0 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: 3 X= 0 3 (b) Use backsubstitution to solve the system in part (a) and find the...

Problem 6 (18 pts.): Let A be a 4 x 2 matrix given by: -1 -5...

Problem 6 (18 pts.): Let A be a 4 x 2 matrix given by: -1 -5 1 1 1 A= -1 -1 1 5 a) Compute the Gram-Schmidt QR factorization of A. b) Use the QR factorization to find the least squares solution of Az = 6, where 6= (-2,-1,5,0).
(4.2) Let 4 7 A= 4 7 -2 1 (a) Find the QR decomposition of A....

(4.2) Let 4 7 A= 4 7 -2 1 (a) Find the QR decomposition of A. It has to be of the form A QR where Q is a 3 x 3 orthogonal matrix, and R is 3 x 2 upper-triangular. (b) Use part (a) to find the least squares solution to the -6 Ax -4 -2
linear algebra question 0. Given 1 3-5 1 1 -2 1-3 1 and b If the Gram-Schmidt process is applied to determine an orthonormal basis for R(A), and a QR factoriza- tion of A then, after the first two or...

linear algebra question 0. Given 1 3-5 1 1 -2 1-3 1 and b If the Gram-Schmidt process is applied to determine an orthonormal basis for R(A), and a QR factoriza- tion of A then, after the first two orthonormal vectors qi and q are computed, we have 2 -2 2 2 2 2 2 (a) Finish the process. Determine q3 and fill in the third columns of Q and R (b) Use the QR factorization to find the least...

Please step by step solution!!! Cholesky factorization versus QR factorization. In this problem we compare the accuracy of the two methods for solving a least-squares problem minimize Ar - b We take...

Please step by step solution!!! Cholesky factorization versus QR factorization. In this problem we compare the accuracy of the two methods for solving a least-squares problem minimize Ar - b We take b10- 1-10-k ke A10 0 10k for k 6, k- 7 and k 8. (a) Write the normal equations, and solve them analytically (i.e., on paper, without using MATLAB). (b) Solve the least-squares problem in MATLAB, for k = 6. K-7 and k = 8, using the recommended...
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR deco...

7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3 7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3
Problem 4: (20 points) Let [ 3 -6 A= 4 -8 0 1 1) Find a...

Problem 4: (20 points) Let [ 3 -6 A= 4 -8 0 1 1) Find a QR-decomposition of A. 2) Use the QR-decomposition that you found in part 1 to find the least squares solution of the system 3 -6 4 - 8

2 3 3. Let A = 2 4 and b = 3 . Find QR factorization...

2 3 3. Let A = 2 4 and b = 3 . Find QR factorization of A. (1 1