Game Development Reference
In-Depth Information
Working with a 2-by-3 Matrix
A matrix provides a convenient way to systematically solve for the values of a
system. Your activity in this respect proceeds in the same way that it did when
you worked with systems of equations and left the variables visible. When you
work with matrices, however, you work with a system that consists of rows and
columns, and the goal of your activity is to arrive at matrices that take the
following form:
2
3
100
j
a
10
j
x
4
5
010
j
b
or
01
j
y
001
j
c
Accordingly, for each row in the matrix, you proceed with multiplication and
addition activities, as you did in the previous section, and your goal is to elim-
inate all values save those that correspond to one of the columns and the final
column. The final column provides you with a variable value.
The system of equations presented in the previous section appears as follows:
3
x
4
y ¼
1
5
x þ
2
y ¼
19
The matrix you create using its coefficients assumes this form:
3
41
5219
To solve for the values of this matrix, you begin by examining the first row and
determining a value that allows you to transform the 3 into 1. This value is the
multiplicative inverse of 3, which is
1
3
. Accordingly, when you carry out this
multiplication, you arrive at this matrix:
4
3
1
3
1
5
2
19
You can then proceed to evaluate the second row. Your goal is to discover the
number by which you can multiply the first row in order to eliminate a column.
You seek a number that allows you to transform the first row so that you can
add it to the second and eliminate the value (5) in the first column. This number
