Graphics Reference
In-Depth Information
Now let's compute
BA
1
×
5
+
2
×
71
×
6
+
2
×
8
BA
=
3
×
5
+
4
×
73
×
6
+
4
×
8
19
22
=
43
50
which confirms that, in general, matrix multiplication is non-commutative.
It can also be shown that
T
B
T
A
T
[
AB
]
=
and
T
A
T
B
T
.
[
+
]
=
+
A
B
4.8 The Inverse Matrix
Most mathematics software systems include a matrix inversion package, but for
completeness, let's demonstrate how we arrived at the inverse matrix
A
−
1
(
4.5
):
13
4
.
1
14
A
−
1
=
−
2
Initially, we started with the simultaneous equations
2
x
+
3
y
=
18
(4.6)
4
x
−
y
=
8
.
(4.7)
Solving these algebraically we multiply (
4.7
) by 3 and add it to (
4.6
) to eliminate
y
:
2
x
+
3
y
=
18
12
x
−
3
y
=
24
14
x
=
42
x
=
3
.
Substituting
x
=
3in(
4.6
)gives
6
+
3
y
=
18
=
which makes
y
4.
4.8.1 Calculation of Inverse
Now let's solve (
4.6
) and (
4.7
) using matrix notation. We begin with
Av
=
c
