# 1.5 Game 2302-0115: working with column matrices, points, and

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Learn how to compare column matrices for equality, compare two points for equality, compare two vectors for equality, add one column matrix to another, subtract one column matrix from another, and get a displacement vector from one point to another.

## Preface

This module is one in a series of modules designed for teaching GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX.

What you have learned

In the previous module, you learned how to update the game-math library to provide new capabilities including the addition of graphics and set methods for column matrices, points, vectors, and lines. You also learned how to draw onoff-screen images.

What you will learn

In this module, you will learn how to compare column matrices for equality, compare two points for equality, compare two vectors for equality, add onecolumn matrix to another, subtract one column matrix from another, and get a displacement vector from one point to another.

## Viewing tip

I recommend that you open another copy of this module in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

## Figures

• Figure 1 . Screen output from the program named ColMatrixEquals01.
• Figure 2 . Screen output from the program named DisplacementVector01.
• Figure 3 . Screen output from the program named ColMatrixAddSubtract01.
• Figure 4 . Text output from Exercise 1.
• Figure 5 . Text output from Exercise 2.
• Figure 6 . Text output from Exercise 3.

## Listings

• Listing 1 . Overridden equals method of the GM2D03.ColMatrix class.
• Listing 2 . Overridden equals method of the GM2D03.Point class.
• Listing 3 . The getColMatrix method of the GM2D03.Point class.
• Listing 4 . Beginning of the ColMatrixEquals01 class.
• Listing 5 . Remainder of the ColMatrixEquals01 class.
• Listing 6 . The getDisplacementVector method of the GM2D03.Point class.
• Listing 7 . The program named DisplacementVector01.
• Listing 8 . Source code for the program named ColMatrixAddSubtract01.
• Listing 9 . Source code for the add method of the GM2D03.ColMatrix class.
• Listing 10 . Source code for the subtract method of the GM2D03.ColMatrix class.
• Listing 11 . Source code for game-math library named GM2D03.
• Listing 12 . Source code for the program named ColMatrixEquals01.
• Listing 13 . Source code for the program named DisplacementVector01.
• Listing 14 . Source code for the program named ColMatrixAddSubtract01.

## Preview

As mentioned earlier, in this module you will learn how to:

• Compare two column matrices for equality.
• Compare two points for equality.
• Compare two vectors for equality.
• Add one column matrix to another.
• Subtract one column matrix from another.
• Get a displacement vector from one point to another.

#### Questions & Answers

show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has \$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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