Game Development Reference
In-Depth Information
Working with a 3-by-4 Matrix
To work with 3
4 matrices, you follow the same path you follow with 2
3
matrices. The only difference is that a few more steps are involved. Consider, for
example, this system of equations:
x y þ
5
z ¼
6
3
x þ
3
y z ¼
10
x þ
3
y þ
2
z ¼
5
If you transform this into a 3
4 matrix, you assign values of 1 to the appropriate
coefficients and drop the variables:
1
15
6
33
1 0
1325
To develop a solution set for this matrix, your goal involves arriving at a matrix
that possesses this form:
2
3
100
j
a
4
5
010
j
b
001
j
c
For each row, then, you seek to transform the values so that you see a 1 and a
corresponding value.
For the current matrix, the first column of the first row is already set to 1, so you
can shift your attention to the second row. You find a value by which you can
multiply the first row that allows you to eliminate the first element from the
second row. This value is
3. To multiply the first row by this value, your actions
take the following course:
1
1
5
6
33
15
18
Multiply first row by
3
:
You then add the transformed version of the first row to the second row:
33
1 0
33
15
18
06
16
28
Result of the addition
:
