Graphics Reference
In-Depth Information
where
23
4
,
x
y
,
18
8
.
A
=
v
=
c
=
−
1
Next we introduce an identity matrix, which does not disturb anything:
Av
=
Ic
(4.8)
23
4
x
y
10
01
18
8
.
=
(4.9)
−
1
The objective is to multiply both sides of (
4.8
)by
A
−
1
and turn the LHS matrix
A
into an identity matrix, and at the same time turn the RHS matrix
I
into
A
−
1
.But
as we don't know
A
−
1
we will have to do this in a number of steps. Like the above
simultaneous equations, we can scale, add, subtract or divide matrix rows, so long
as we manipulate the entire matrix equation.
We start by subtracting 2
×
row(
1
)
from
row(
2
)
in (
4.9
):
23
0
x
y
18
8
.
10
=
(4.10)
−
7
−
21
7
3
Next, multiply
row(
1
)
×
in (
4.10
):
1
3
x
y
18
8
.
7
3
7
0
=
(4.11)
−
0
−
7
21
Next, add
row(
2
)
to
row(
1
)
in (
4.11
):
1
3
x
y
18
8
.
1
3
0
1
=
(4.12)
0
−
7
−
21
3
Next, multiply
row(
1
)
×
14
in (
4.12
):
10
0
x
y
18
8
.
1
14
3
14
=
(4.13)
−
7
−
21
Finally, divide
row(
2
)
by
7in(
4.13
):
10
01
−
18
8
x
y
.
1
14
3
14
=
(4.14)
2
7
1
7
−
As the LHS matrix is an identity matrix, the RHS matrix in (
4.14
)mustbe
A
−
1
and
is tidied up to become
13
4
.
1
14
A
−
1
=
−
2
Later on, we will explore another technique that does not involve any overt algebraic
skills.
