Jerry had a long week at school and is excited that it is the weekend. He decides, after studying for hours for his math quiz, to take a break and play his favorite video game, “Dragons vs Fairies”

Oh yeah, I'll take a break this weekend.

Math 235 Review

Done

Quiz: Next Wednesday

Jerry gets his snacks, his controller and sits on his gaming chair ready to defeat the dragons.

 Let's defeat the dragon!

But something strange happens! The computer screen suddenly lights up with spiraling lights.

OMG What is going on!?

Jerry sits in shock at what he is seeing, when all of a sudden, he gets sucked into the screen!

Ahhhhhhhhhh

Now Jerry is a part of the game! Now, this is where we come in. We are going to help Jerry defeat the dragons and escape the video game.

HELP!!!

Now the video game is in a 3-dimensional world and Jerry lives in a 2-dimensional world. So in order to get out of the game, Jerry needs to find a secret key or machine that could transform him from 3D to 2D. Could you help Jerry get back home?

I Want to go back to my 2D world.

Game Tips: Find a secret key to escape the 3D world.

The game is set in the mystical land of “Lavaz” where fairies and dragons live side by side. At one time they lived harmoniously with one another, but as time passed, the dragons grew hungry for power over the land and started a war to take full control.

Good morning Mr. Green.

Now Jerry is stuck in the middle of this battle for power. Jerry enters the game as a fairy as he selected that option when he was setting up the game before.

In Lavaz, Jerry meets Prince Teq, leader of the fairies. Jerry quickly tells Prince Teq that he is from another dimension and wants help to get back home. Prince Teq agrees to help Jerry and has a machine that could help. However the machine is now broken and Jerry will need to help fix it if he wants to get out of the game.

Our sacred vessel may help you go back to your world young fairy, but it was broken in the First Lavaz Resistance. We must find a way to fix it.

I really appreciate it, Prince Teq.

Prince Teq's Secret Base

In order for this machine to work, it must have specific numbers in all 16 spots. If the wrong numbers are put in, Jerry could end up in another dimension or get lost in space and time.

Prince Teq's Secret Base

 If we look at the machine, it is missing two numbers. Jerry needs your help to fix it so he can get back home.

Prince Teq's Secret Base

Prince Teq tells Jerry of an old wise fairy named Spart that could help him fix the machine.

Spart should know how to fix it.

Jerry goes to visit Spart to see if he could help. Jerry tells Spart that he wants to go home and his machine is broken, so Spart says he will try to help.

But Spart says his knowledge is limited and that he only has part of the information to reconstruct the machine. Spart gives him an old rustic blueprint for the machine, but it's worn...

Blueprint for the Dimensionator

Jerry, as you can see, this machine when it is fixed can take you from 3D to 2D. The colorful points are called vertices. The vertices in the 3D world will match with vertices in the 2D world with the same color. We can name vertices. For example, in the 3D world all vertices look like [x y z 1]. The black vertex in the 3D world is called [0 0 -n 1]. The machine will transform this vertex into the 2D vertex  [0 0 1]. You are also made up of vertices. So the machine will change all your vertices from 3D to 2D. I hope this gives you a clue to get back home. Good luck!

Just as Jerry leaves Spart’s house, he is captured by a dragon and is locked inside a cage. The dragon gives him a puzzle to solve if he wants to escape. He has to solve this puzzle by the end of the day or he will be eaten. This is the puzzle:

Solve this puzzle to get out. What is a, b and c?

This puzzle is called a Matrix Multiplication. We are going to help Jerry solve this puzzle and escape!

This matrix has 3 rows. The red arrows point to row 1, row 2 and row 3

This matrix has 3 columns. The blue arrows point to column 1, column 2 and column3

The puzzle was color coded for us. To solve for a, we must use column 1. To solve for b, we must use column 2, and to solve for c, we must use column 3. We need to multiply [1 2 3] by each of these to solve the problem:

But how do we multiply matrices? 

To do matrix multiplication here, we multiply the numbers which match in color and then add them altogether. We find that a = 7. Now we must find b and c.

We do the same thing to solve for b

Try to solve for c in the same way. 

You should get 6!

I solved the puzzle! a= 7, b=9 and c=6.

That's correct! Aw man, I was really looking forward to a yummy dinner! But now, I'll keep my promise and let you go.

Jerry solves the puzzle and the dragon lets him out of the cage. Now Jerry can continue fixing the machine!

As Jerry escapes the cage, he meets back up with Prince Teq. Prince Teq asks him if Spart was able to help. Jerry shows him the blueprint and said he still needs to find the missing pieces a and b. Prince Teq tells him of a troll in a cave who might have stolen the missing pieces in the last resistance. However, Jerry would have to solve a puzzle to get it!