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Chapter 2 – Systems of Linear Equations
Section 2.1 – Introduction to Systems of Linear Equations
Pg 59, Definition – A
linear equation
in the n variables is an equation that can be written in the form
where the
coefficients
and the
constant term
b are constants.
Pg 61, A system of linear equations with real coefficients has either
(a) a unique solution (a consistent system) or
(b) infinitely many solutions (a consistent system) or
(c) no solutions (an inconsistent system).
Pg 61, Two linear systems are called
equivalent
if they have the same solution sets.
Section 2.2 – Direct Methods for Solving Linear Systems
Pg 68, The
coefficient matrix
contains the coefficients of the variables, and the
augmented matrix
has an extra
column containing the constant terms.
Pg 68, Definition – A matrix is in
row echelon form
if it satisfies the following properties:
1.
Any rows consisting entirely of zeros are at the bottom.
2.

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