I
NTRODUCTION
TO
M
ATRICES
Linear algebra is the art of solving systems of linear equations.
For smaller systems, we have
used substitution, elimination, and graphing.
For larger systems it is necessary to use more
systematic methods.
To solve larger systems of linear equations we use
matrices
(we used
this a little to solve systems of three linear equations on the GDC).
Ex
.
You are given a set of three linear equations in three variables to solve.
1
10
4
5
5
2
2
4
8
2
=

+
=
+
+
=
+
+
z
y
x
z
y
x
z
y
x
To solve this system, a computer needs only the coefficients of the variables and the constant
terms.

1
1
10
4
5
1
5
2
2
4
8
2
This array of numbers is called a
matrix
.
The matrix has 3 rows and 4 columns so it is called
a 3 x 4 matrix.
This is referred to as the
order
of the matrix and is given as
n
m
×
where
m
is
the number of rows and
n
is the number of columns.
.
The first column of the matrix corresponds to the first variable,
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