Game Development Reference
In-Depth Information
You can now reach the first of the major goals of your operation, which is to
discover the value that corresponds to the third row. Toward this end, you
multiply the third row by the multiplicative inverse of
2
3
. Here is the matrix that
results from this operation:
10
7
4
3
3
14
3
00 1
1
8
3
01
Given that you know the value of the third element in the third row, you can
multiply this row by
7
3
to create a set of values you can add to the first row to
eliminate the third element from that row. The result of the multiplication is as
follows:
7
3
7
3
00
When you add this row to the first, your matrix that results takes this form:
10 0 1
14
3
00 1
1
8
3
01
To eliminate the third element from the second row, you multiply the third row
by
3
. The result of the multiplication takes this form:
00
8
3
8
3
When you add this to the second row, your matrix then assumes its final form:
1001
0102
001
1
You can write the solution values for this matrix as
x ¼
1,
y ¼
2, and
z ¼
1.
