Graphics Reference
In-Depth Information
where
=+
=−
a
22
a
23
14
26
A
11
=+
2
a
32
a
33
=−
=
a
21
a
23
24
46
A
12
=−
4
a
31
a
33
=+
=
a
21
a
23
21
42
A
13
=+
0
a
31
a
33
=−
=
a
22
a
23
13
26
A
21
=−
0
a
32
a
33
=+
=−
a
11
a
13
03
46
A
22
=+
12
a
31
a
33
=−
=
a
12
a
11
01
42
A
23
=−
4
a
31
a
32
=+
=
a
12
a
13
13
14
A
31
=+
1
a
22
a
23
=−
=
a
11
a
13
03
24
A
32
=−
6
a
21
a
23
=+
=−
a
11
a
12
01
21
A
33
=+
2
a
21
a
22
therefore, the cofactor matrix of
A
is
⎡
⎤
−
2
4
0
⎣
⎦
.
cofactor matrix of
A
=
0
−
12
4
1
6
−
2
It can be shown that the product of a matrix with the transpose of its cofactor matrix
has the following form:
⎡
⎣
⎤
⎦
det
A
0
...
0
0
det
A
...
0
A
(
cofactor matrix of
A
)
T
=
...
...
...
...
0
0
0
det
A
and multiplying throughout by 1
/
det
A
we have
(
1
/
det
A
)
A
(
cofactor matrix of
A
)
T
=
I
which implies that
(
cofactor matrix of
A
)
T
det
A
A
−
1
=
.
Naturally, this assumes that the inverse actually exists, and it will if det
A
=
0.
