Solve the system Ux = y for x. U = ? X = ? 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, then the system Ax = b can be expressed as LUX = b and can be solved in two steps: Step 1. Let Ux = y, so that LUX = b can be expressed as Ly = b. Solve this...
In this exercise you will work with LU factorization of an matrix A. Theory: Any matrix A can be reduced to an echelon form by using only row replacement and row interchanging operations. Row interchanging is almost always necessary for a computer realization because it reduces the round off errors in calculations - this strategy in computer calculation is called partial pivoting, which refers to selecting for a pivot the largest by absolute value entry in a column. The MATLAB...
1 00] 11 0 -1] 6. Suppose L = 0 1 0, U = 0 1 2 and b = 2. Solve LUX =b for x. Only half 2 LO 0 1 credit if you first find the product LU as part of your solution. que
True or False 1. If u, v are vectors in R"and lu + v1l = ||||| + ||v||, then u and v are orthogonal. 2. If p locates a point on a line l in Rand if n # 0 is normal to l, then any other point x on I must satisfy n.x=n.p. 3. A binary vector is a vector with two components which are integers modulo 2. 4. The set of solution vectors to the linear system Ax=b...
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
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
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...
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equations (la)-(1c) model? (Hint: Give an interpretation for the PDE, boundary conditions and intial condition.) c) Use the method of separation of variables to separate the above problem into two sub- problems (one that depends on space and the other only on time) (d) What...
3 (The UL factorization.) Show how to compute the factorization A = UL where U is upper triangular with ls along the diagonal and L is lower triangular. Show how this relates to a way of solving Ax = b by transforming the system into an equivalent system with a lower triangular matrix. (In other words, show that what we did for the LU factorization also works for a UL factorization.) Note: For the purposes of this exercise you may...
Problem 3. Suppose A has eigenvalues 0, 3, 5 with corresponding independent eigenvectors u, v,w. (a) Give a basis for the nullspace and a basis for the column space. (b) Find a particular solution to Ax=y+w. Also, find all solutions to Ax=y+w.