Graphics Reference
In-Depth Information
Let's find the inverse of the above matrix
⎡
⎤
013
214
426
⎣
⎦
A
=
⎡
⎤
−
2
4
0
⎣
⎦
(
cofactor matrix of
A
)
=
0
−
12
4
1
6
−
2
⎡
⎤
−
2
0
1
(
cofactor matrix of
A
)
T
⎣
⎦
=
4
−
12
6
0
4
−
2
=
×
×
+
×
×
−
×
×
−
×
×
=
det
A
1
4
4
3
2
2
1
2
6
3
1
4
4
⎡
⎤
−
2
0
1
1
4
A
−
1
⎣
⎦
.
=
4
−
12
6
0
4
−
2
Let's check this result by multiplying
A
by
A
−
1
which must equal
I
:
⎡
⎤
⎡
⎤
013
214
426
−
2
0
1
1
4
AA
−
1
⎣
⎦
⎣
⎦
=
4
−
12
6
−
0
4
2
⎡
⎤
400
040
004
1
4
⎣
⎦
=
⎡
⎤
100
010
001
⎣
⎦
.
=
Finally, let's compute the inverse matrix for (
4.6
) and (
4.7
) using cofactors:
23
4
A
=
−
1
−
1
−
4
(
cofactor matrix of
A
)
=
−
32
−
1
−
3
(
cofactor matrix of
A
)
T
=
−
42
det
A
=
2
×
(
−
1
)
−
3
×
4
=−
14
13
4
1
14
A
−
1
=
−
2
which confirms the original result.
In general, the inverse of a 2
×
2 matrix is given by
a
11
a
12
=
A
a
21
a
22
