Let A be an m × n matrix. Prove that every vector x in Rn can be written in the form x = p+ u, where p is in Row A and u is in Nul A. Also, show that if the equation Ax = b is consistent, then there is a unique p in Row A such that Ap =b.
Let A be an m × n matrix. Prove that every vector x in Rn can be written in the form x = p+ u, where p is in Row A and u is in Nul A. Also, show that if the equation Ax = b is consistent, then there is a unique p in Row A such that Ap =b.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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