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NOTES ON SECTION
1
.
2
MA265, SECTIONS 41, 52
Overview: this section introduces systems of equations, summarizes the solution process, and describes
the possible solution sets.
Key words
Matrix
Equal matrices
diﬀerence of matrices
rows
n
vector
summation notation
columns
R
n
,
C
n
Index of summation
size of a matrix
0
, zero vector
linear combination
square matrix
Google
coeﬃcients
main diagonal
addition of matrices
transpose
entry of a matrix
scalar multiple
A matrix is a box of numbers, e.g.:
B
=
1
3
π
e

2
3
.
122
0
0
0
ln(2)
ln(
π
)
e
π
This matrix has 4
rows
and 3
columns
. We say it has
size
4
×
3. The 2
nd
row is
±
e

2
3
.
122
²
and the 3
rd
column is
π
3
.
122
0
e
π
A general matrix looks like this:
A
=
a
11
a
12
...
a
1
n
a
21
a
22
...
a
2
n
a
31
a
32
...
a
3
n
.
.
.
.
.
.
.
.
.
a
m
1
a
m
2
...
a
mn
The
i
th
row is
±
a
i
1
a
i
2
...
a
in
²
and the
j
th
column is
a
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