Game Development Reference
In-Depth Information
Exercise Set 11.8
Here are some systems of equations with three values that you can solve using matrices.
a. 4x y þ 3z ¼3
3x þ y þ z ¼ 0
2x y þ 4z ¼ 0
b. x 2y þ 3z ¼ 4
5x þ 7y z ¼ 2
2x þ 2y 5z ¼ 3
c. x þ y þ z ¼ 4
2x y 3z ¼ 4
4x þ 2y z ¼ 1
d. x 2y 3z ¼ 3
2x y 2z ¼ 4
4x þ 5y þ 6z ¼ 4
e. 3x þ 2y þ 2z ¼ 3
x þ 2y z ¼ 5
2x 4y þ z ¼ 0
Conclusion
In this chapter, you have investigated how to solve equations that contain two
variables. A central approach in this respect involves substitution. Accordingly,
you solve an equation for one of its values, and then substitute the solution back
into the equation to solve for the remaining value. Working with substitution
provided a starting point for examining systems of equations. Systems of
equations can involve any number of different variables. They can also involve
any number of equations.
In this chapter, you started out by examining how to work with systems of two
equations. You then moved to three. You first used multiplication and addition
to approach equations as sets of variables with coefficients. From this you pro-
ceeded to examine systems of equations on a different basis. This basis involved
matrices. By considering only the coefficient values of systems of equations, you
could generate the elements of matrices. In this chapter, you concentrated on
working with 2
3 and 3
4 matrices. While matrices of much larger dimen-
sions exist, working with these has introduced you to the skills that prove most
primary in working with systems of equations.
