Biology Reference
In-Depth Information
0
@
1
A
e
1
e
2
.
We multiply a row matrix (a
1
, a
2
,
...
, a
n
) by a column matrix
according to:
0
1
e
n
e
1
e
2
.
@
A
ð
a
1
;
a
2
;
...
;
a
n
Þ
¼
a
1
e
þ
a
2
e
þ
...
a
n
e
:
1
2
n
e
n
Note there are the same number of entries in both matrices. Also, the
''row matrix'' must be on the left, and the ''column matrix'' must be on
the right. In the context of our discussions, we would like to think
of the a
i
's as numbers and the
e
i
's as unknowns.
Now suppose we have two linear equations where the unknowns
are
e
1
,
e
2
,
,
e
n
:
...
a
11
e
þ
a
12
e
þ
...
þ
a
1n
e
¼
b
1
1
2
n
b
2
:
(8-60)
a
21
e
þ
a
22
e
þ
...
þ
a
2n
e
¼
1
2
n
We define:
0
@
1
A
e
1
e
2
a
11
a
12
...
a
1n
a
11
e
þ
a
12
e
þ
...
þ
a
1n
e
1
2
n
¼
;
a
21
a
22
...
a
2n
.
e
a
21
e
þ
a
22
e
þ
...
þ
a
2n
e
1
2
n
n
so we could write the system of Eq. (8-38) as the matrix equation.
0
@
1
A
e
1
e
2
:
a
11
a
12
a
1n
b
1
b
2
...
¼
.
a
21
a
22
a
2n
...
e
n
This is often written in the more compact form A
e ¼
b, where A, b, and
e
are the following matrices:
0
1
e
1
e
2
.
@
A
:
a
11
a
12
a
1n
b
1
b
2
...
A
¼
; e ¼
;
b
¼
a
21
a
22
a
2n
...
e
n
