4. Find a QR-factorization of the matrix 5. Find an LU-decomposition of the 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 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=
5. (a) (5 marks) Find the LU factorization of the matrix A = 1 1 14 -1 -1 -4 21 3 where L is a unit 7 lower triangular matrix and U is an echelon form of A. (b) (5 marks) Use the LU factorization found in part (a) to solve Ax =
Write Matlab script for computing inverse of a matrix using LU decomposition/factorization. You are not allowed to use the Matlab’s lu function.
Find the LU-factorization of the matrix. (Your L matrix must be unit diagonal.) 4 0 1 8 1 1 L-4 1 0] LU = It
Question 3. [3 marks ] Use the MATLAB built-in LU matrix factorization function "lu" to find the PLU factorization of the matrix below 1 -2 30 1 -2 3 1 2 22 2 3 Question 3. [3 marks ] Use the MATLAB built-in LU matrix factorization function "lu" to find the PLU factorization of the matrix below 1 -2 30 1 -2 3 1 2 22 2 3
Find an LU factorization of the matrix A (with L unit lower triangular) [ -4 0 2 A= 12 2 - 1 12 10 27 L=0
5. Let T E Rxn be a nonsingular symmetric tridiagonal matrix, T -QR be a QR factorization of T and S- RQ. (a) Show that S is also a nonsingular symmetric tridiagonal matrix. (b) How many operations (addition, subtraction, multiplication, and division) are required to ob- tain S from T? 5. Let T E Rxn be a nonsingular symmetric tridiagonal matrix, T -QR be a QR factorization of T and S- RQ. (a) Show that S is also a nonsingular...
Let A be a tri-diagonal matrix. Find the LU factorization of A and calculate the number of FLOPs needed for the factorization.
1. (4) Find the QR decomposition of the matrix A = -1 0 2 1
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...