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(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 € null(A). (b) Let A be an m x n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.

(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 € null(A). (b) Let A be an m x n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 = null(A). (b) Let A be an m × n matrix, and let B be an n × p matrix. Prove that (AB)T = BT 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 = null(A). (b) Let A be an m × n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.
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