Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every solution of Ax =b can be written as x = p+z where z E null(A). Let A be an m x n matrix, and let B be an n × p matrix. Prove that (AB)™ = B" A".

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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1. (a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every
solution of Ax = b can be written as x =p+z where z E null(A).
(b) Let A be an m x n matrix, and let B be an n x p matrix. Prove that (AB)" = B™ AT.
Transcribed Image Text:1. (a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every solution of Ax = b can be written as x =p+z where z E null(A). (b) Let A be an m x n matrix, and let B be an n x p matrix. Prove that (AB)" = B™ AT.
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