Math 205, Spring 2006
B. Dodson
New text  PetersonSochacki
———
1. Course Info
2. Week 1 Homework:
1.1 (1st half), 1.2 Intro
Due Thurs!
———
An
m
×
n
matrix
A
is an array
with
m
horizontal rows;
n
vertical columns
i, j
th entry
a
i,j
in the
i
th row, and
j
th column.
row vector
or row
n
vector,
a,
is a 1
×
n
matrix, just one row.
column vector
or column
n
vector,
b,
is a
n
×
1 matrix, just one column.
———
Example. Give the rows and columns of
A
=
2
10
6
5

1
3
¶
.
What are the entries
a
1
,
2
, a
2
,
1
, a
3
,
1
, a
1
,
3
?
The matrix sum,
A
+
B,
is defined only when
A
and
B
have the same shape; and then the
i, j
th entry of
A
+
B
is
a
i,j
+
b
i,j
,
the sum of the
i, j
th entries of
A
and
B.
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2
The scalar multiple of the matrix
A
by the scalar
(number!)
c
is the matrix with the same shape as
A,
but with
i, j
th entry of
ca
i,j
.
Matrix multiplication: 1. row
n
vector by column
m
vector, only when
n
=
m,
is the number
a
1
b
1
+
a
2
b
2
+
· · ·
+
a
n
b
n
,
where the
a
i
are the entries of
a
and the
b
i
are
the entries of
b.
2.
m
×
n
matrix
A
by
p
column vector
b,
only when
n
=
p,
is the
m
column vector with
i
th entry (
i
th row of
A
)
·
b.
——–
Problem 3.2.11
Multiply
A
=

1
2
4
7
5

4
by
c
=
5

1
¶
.
Solution:
Ac
=

1
2
4
7
5

4
5

1
¶
=
(

1)(5) + 2(

1)
4(5) + 7(

1)
5(5) + (

4)(

1)
=

7
13
29
.
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 Spring '08
 zhang
 Math, Linear Algebra, Algebra, Row, elementary row operations

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