Math 43, Fall 2007
B. Dodson
Week 7:
Graded Homework 7:
3.1  14; 3.2  24; 3.3  2.
due Mon. Oct. 22
Suggested Homework 7:
graded Homework plus
3.1  3, 4, 5, 15, 23, 35;
3.2  1, 2, 23; 3.3  3, 11, 35
due Wed. Oct. 24.
Seventh week. Matrix Arithmetic; Algebra; Inverses
If
A
and
B
are both
m
by
n
matricies,
with
A
= [
a
i,j
] and
B
= [
b
i,j
] the matrix sum
C
=
A
+
B
is the matrix
C
= [
c
i,j
] with
i, j
th entry
c
i,j
=
a
i,j
+
b
i,j
.
We also have scalar multiplication
rA,
which has
i, j
th entry
ra
i,j
.
For
matrix multiplication,
multiplying two matricies, we start
with rowmatrix
×
columnmatrix by
[
r
1
, r
2
, . . . , r
n
]
×
c
1
c
2
. . .
c
n
=
r
1
c
1
+
r
2
c
2
+
···
+
r
n
c
n
.
For example [2
,

1]
3
2

1
=
. . .
and [2
,

1
,
5]
3
2

1
=
. . .
Finally, if
A
has rows
±
R
1
. . .
±
R
s
and
B
has columns
B
= [
±
C
1
, . . . ,
±
C
u
] we set
AB
=
A
[
±
C
1
, . . . ,
±
C
u
] = [
A
±
C
1
, . . . , A
±
C
u
] which is the matrix with entries
±
R
i
±
C
j
,
.