(a) Suppose we want to change columns 6 and 7 in our matrix A. Express the new matrix as A - ZVT, where Z and V have dimension n × 2. (b) Suppose we want to change both column 6 and row 4 of A. Find Z and V so that our new matrix is A - ZVT.

(a) Suppose we want to change columns 6 and 7 in our matrix A. Express the new matrix as A - ZVT, where Z and V have dimension n × 2. (b) Suppose we want to change both column 6 and row 4 of A. Find Z and V so that our new matrix is A - ZVT.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.1: Matrices And Vectors

Problem 5P

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Concept explainers

LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.

Question

(a) Suppose we want to change columns 6 and 7 in our matrix A. Express the new matrix
as A - ZVT, where Z and V have dimension n × 2.
(b) Suppose we want to change both column 6 and row 4 of A. Find Z and V so that our
new matrix is A - ZVT.

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