8. Factor the following matrices into PA= LU. Also factor them into A=LP U1. A= [120]...
Factor the following matrices into LU form 2 -3 1-3 (b) 2 2 2
Which of the following pairs is the solution to the LP problem: min U1 + 2u2 subject to: 3u1+U227 U1+442 26 U1U220 o (u1, u2) = (2, 1) O (u1, u2) = (1, 4) o (u1, u2) = (6,0) 0 (u1, u2) = (0,7)
Problem 2 (a) Find the LU factorization of the following matrix, then verify your answer by computing LU -1 4 5 a) 6 2 -4 1 -21 (b) Find the determinants of the following matrices. Show all your calculations and steps: [-1 4 51 a)6 2 -4b) 0 6 8 2 -4 3 3 2 6 8 10
(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...
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...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1 (a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
1. Algebra: Solve the system of equations given by Ax = b, using the LU factorisation given for A, where [ 2 -1 27 [1 00] [2 -1 2] A= -6 0 -2, b= 0 and A= -3 1 0 0 -3 4. [ 8 -1 5 4 [ 4 -1 1 0 0 1 2. Algebra: Find an LU decomposition of the matrices (i) [1 1 4 3 3 5 11 -1 3 (ii) 1-5 341 10 -8 -9....
matrices multiplication in matlab only A&C Consider three matrices: A = [6 -1 12 8 -5 6] B = [4 0 0.5 1] C = [2 -2 -3 1] Perform all possible multiplications that can be computed between these pairs of matrices. Perform the multiplications in Matlab and check the result by hand (showing work). Use the method in Box PT3.2 to justify why the remaining pairs cannot be multiplied. Perform the comparisons B > C and B < C...
Formulate the following problems as LP problems. (Do not solve them, just formulate) raw materials available in the following *c) A chemical processing plant has three types of (liquid) amounts Type of raw material Amount in ounces A 3,000 5,000 12,000 B from which will be blended five grades of perfumes whose compositions are given below Perfume grades -» 2 3 4 5 Percentage of material A Percentage of material B Percentage of material C 90 80 50 30 10...
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...