Solve the system Ux = y for x. U = ? X = ? If the...

Question

Question

If the nxn matrix A can be expressed as A = LU, where L is a lower triangular matrix and U is an upper triangular matrix, the

Solve the system Ux = y for x.

U = ?

X = ?

math algebra

Answer 1

Answer #1

A : LU 1 Ora -1 47 -1 4 ollo a 3 L1 @11 Loo L: [2007 3 -1 47 -1 40 To 23 Li a 1] LO o 9]. uzc. [3 -1 410] [32,-X+4x37 oa 3

Answer 2

Similar Homework Help Questions

2. Solve the linear system Ax = B, by, (20P) a) Finding LU-factorization of the coefficient...

2. Solve the linear system Ax = B, by, (20P) a) Finding LU-factorization of the coefficient matrix A, b) Solving the lower triangular system Ly = b, c) Solving the upper triangular system Ux = y. where w A = 2 0 0 0 -2 1 0 2 0 0 0 0 - 1 1 1 4. -4 15 and b =
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equa...

(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
Solve the equation Ax b by using the LU factorization given for A. Also solve Ax...

Solve the equation Ax b by using the LU factorization given for A. Also solve Ax b by ordinary row reduction. 3 -5 1 0 0 3 5 4 4 A = 19 -3 1 3 -1 1 0 0 - 4 1 6 2 -6 2 3 1 0 1 58 - Let Ly b and Ux y. Solve for x and y. y X = Row reduce the augmented matrix [A b] and use it to find x...

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...
Solve the equation Ax = b by using the LU factorization given for A. 0 0...

Solve the equation Ax = b by using the LU factorization given for A. 0 0 2 - 4 - 2 12 -4 -2 0 10 A=1 - 4 2. 2 0-2 b = 3 3 -4 -3 0 0 3 6 -1 1 2 لیا Let Ly = b. Solve for y y = Let Ux = y. Solve for x. X=
of the y b, and the upper triangular system y 2x y (a) Find an t...

of the y b, and the upper triangular system y 2x y (a) Find an t (c) Solve the upper triangular system Ux y O Type here to search

1. (All students!) For matrices with special properties, it is possible to create special version...

1. (All students!) For matrices with special properties, it is possible to create special versions of Gauss elimination. Suppose matrix A (nxn) is symmetric (which means that A-A). Suppose also that A is positive definite; this means that the scalar = xTAx is always 20 for every vector x , and J-0 only if x = 0 In this case it can be shown that the usual Gauss elimination process, which effectively creates the factorization A LU, can be simplified...
4. (30 points) Consider the following 2 x 2 system Axb (a) (10 points) Use the...

4. (30 points) Consider the following 2 x 2 system Axb (a) (10 points) Use the elimination algorithm discussed in class and on the homework to turn Ax the form Ux = c, where U is an upper triangular matrix and c is a modified version of b. binto (b) (10 points) Continue the elimination algorithm to turn Ux-c from part (a) into the form Dx d. where D is a diagonal matrix and d is a modified version of...
2.5.3 Solve the equation Ax - b by using the LU factorization given for A 4...

2.5.3 Solve the equation Ax - b by using the LU factorization given for A 4 -5 4 1 0 0 4-54 A-8 7-32 13 5 21 12 -12 8 3 -1 1 0 - 24 Let Ly- b and Ux -y. Solve for x and y Enter your answer in the edit fields and then click Check Answer. Clear All

Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0)...

Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) my question please answer Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) Solve the initial-boundary value problem for the following equation Uų...