Homework Answers
(911 (1) (a) Recall that a square matrix A has an LU decomposition if we can...
(911 (1) (a) Recall that a square matrix A has an LU decomposition if we can write it as the product A = LU of a lower triangular matrix and an upper triangular matrix. Show that the matrix 0 1 21 A= 3 4 5 (6 7 9] does not have an LU decomposition 0 0 Uji U12 U13 O 1 2 Il 21 l22 0 0 U22 U23 = 3 4 5 (131 132 133 0 0 U33 6...
1 point) Find the LU factorization of 4 -5 -20 23 That is, write A LU where L is a lower triangular matrix with ones on...
1 point) Find the LU factorization of 4 -5 -20 23 That is, write A LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix A=
1 point) Find the LU factorization of 4 -5 -20 23 That is, write A LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix A=
(1 point) Find the LU factorization of That is, write A = LU where L is...
(1 point) Find the LU factorization of That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following...
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following steps (a)(b) to obtain the LU decomposition of the matrix A with partial piv- oting (a) Apply the Gaussian elimination method with partial pivoting to obtain an upper trian- gular matrix U. Record the corresponding permutation matrix for each pivoting step, and the numbers lik used to eliminate the zeros in column k. (b) Based on (a), express the matrices P, L and U...
(1 point) Find the LU factorization of -g 3 -3 A = 4 LU where L...
(1 point) Find the LU factorization of -g 3 -3 A = 4 LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix. That is, write A A =
suppose we have a) find a factorization of A into the product MU where U is...
suppose we have a) find a factorization of A into the product MU where U is upper triangular (that is, find M and U such that A = MU where U is upper triangular). b) find a permutation matrix P such that PA = LU where L is a lower triangular matrix and U is the same upper triangular matrix found in part a). 0301 3-14 1124 0012
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pi...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
06.Matrix Factorization: Problem 11 Previous Problem Problem List Next Problem (1 point) Find the LU factorization...
06.Matrix Factorization: Problem 11 Previous Problem Problem List Next Problem (1 point) Find the LU factorization of -E 2 2 A 4 That is, write A LU where L is a lower trianqular matrix with ones on the diagonal, and U is an upper triangular matrix A Note: You can eam partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times
Function LUfac_solver.m is provided here: function [x] = LUfac_solver(LU,b,piv) % % function [x] = LUfac_solver(lu,b) %...
Function LUfac_solver.m is provided here:
function [x] = LUfac_solver(LU,b,piv)
%
% function [x] = LUfac_solver(lu,b)
%
% This program employs the LU factorization to solve the linear
system Ax=b.
%
% Input
% LU: lu matrix from GEpivot_new function
% b: right side column vector (ordered corresponding to original
vector
% sent to GEpivot_new)
% piv: vector indicating the pivoting (row interchanges that
took place
% during GE
%
% Output
% x: solution vector
%
% Written by Steve...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutat...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P Use Gaussian elimination with partial pivoting to find an upper triangular matix U, permutation matrices Pi and P2 and lower triangular matrices M and M2 of the form 1 0 0 0 1 1 0 0 0 bi 1 with land...
(911 (1) (a) Recall that a square matrix A has an LU decomposition if we can write it as the product A = LU of a lower triangular matrix and an upper triangular matrix. Show that the matrix 0 1 21 A= 3 4 5 (6 7 9] does not have an LU decomposition 0 0 Uji U12 U13 O 1 2 Il 21 l22 0 0 U22 U23 = 3 4 5 (131 132 133 0 0 U33 6...
1 point) Find the LU factorization of 4 -5 -20 23 That is, write A LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix A=
1 point) Find the LU factorization of 4 -5 -20 23 That is, write A LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix A=
(1 point) Find the LU factorization of That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following steps (a)(b) to obtain the LU decomposition of the matrix A with partial piv- oting (a) Apply the Gaussian elimination method with partial pivoting to obtain an upper trian- gular matrix U. Record the corresponding permutation matrix for each pivoting step, and the numbers lik used to eliminate the zeros in column k. (b) Based on (a), express the matrices P, L and U...
(1 point) Find the LU factorization of -g 3 -3 A = 4 LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix. That is, write A A =
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
06.Matrix Factorization: Problem 11 Previous Problem Problem List Next Problem (1 point) Find the LU factorization of -E 2 2 A 4 That is, write A LU where L is a lower trianqular matrix with ones on the diagonal, and U is an upper triangular matrix A Note: You can eam partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times
Function LUfac_solver.m is provided here:
function [x] = LUfac_solver(LU,b,piv)
%
% function [x] = LUfac_solver(lu,b)
%
% This program employs the LU factorization to solve the linear
system Ax=b.
%
% Input
% LU: lu matrix from GEpivot_new function
% b: right side column vector (ordered corresponding to original
vector
% sent to GEpivot_new)
% piv: vector indicating the pivoting (row interchanges that
took place
% during GE
%
% Output
% x: solution vector
%
% Written by Steve...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P Use Gaussian elimination with partial pivoting to find an upper triangular matix U, permutation matrices Pi and P2 and lower triangular matrices M and M2 of the form 1 0 0 0 1 1 0 0 0 bi 1 with land...
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