Matrix Theory & Applications: For Scientists & Engineers by Alexander Graham

Author:Alexander Graham
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2018-07-21T16:00:00+00:00

Definition 5.4

The matrix whose columns are a1, a2, … an, b, denoted by [A, b], is called the augmented matrix of A.

We can now rephrase Theorem 5.2 into the following form:

Theorem 5.2A

The system of equations (5.6) has a solution if and only if r(A) = r(A,b]).

We now come to the uniqueness problem. Assume we have a particular solution, say y, to (5.6), that is,

and that z is any solution to the corresponding system of homogeneous equations, to Ax = O so that

Next let w = y + z, then

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