Matrix Algebra for Engineers by Jeffrey Chasnov

Author:Jeffrey Chasnov
Language: eng
Format: epub
Publisher: Bookboon.com Ltd.
Published: 2018-07-03T00:00:00+00:00

22 Application of the null space

View this lecture on YouTube

An underdetermined system of linear equations Ax = b with more unknowns than equations may not have a unique solution. If u is the general form of a vector in the null space of A, and v is any vector that satisfies Av = b, then x = u + v satisfies Ax = A(u + v) = Au + Av = 0 + b = b. The general solution of Ax = b can therefore be written as the sum of a general vector in Null(A) and a particular vector that satisfies the underdetermined system.

As an example, suppose we want to find the general solution to the linear system of two equations and three unknowns given by

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.