Welcome guest
You're not logged in.
251 users online, thereof 0 logged in

Application: SLEs Revised in the Light of Vector Spaces

Note that the elementary Gaussian operations $I$ and $II$ correspond to the scalar multiplication and the vector addition, followed by a scalar multiplication. Moreover, if we consider a system of linear equations (SLE) in a vector space $V$, then the following can be said about its solutions:

If the vector $u$ is a solution inhomogeneous system of linear equations $Ax=b,$ then all of its solutions are given by the vectors $y:=u\pm h,$ where $h$ is the solution of the homogeneous system of linear equations $Ah=0.$

In fact, the above statement reformulates in a much shorter notation a theorem stating the relationship between the solutions of homogeneous and inhomogeneous SLEs, which was proved above.

| | | | created: 2018-10-11 18:32:09 | modified: 2018-10-11 18:44:08 | by: bookofproofs

This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:


Bibliography (further reading)

FeedsAcknowledgmentsTerms of UsePrivacy PolicyImprint
© 2018 Powered by BooOfProofs, All rights reserved.