How to determine change in area of matrices tranformations.

[Cacophony]

Homework Statement

Determine what the tranformation does to the square with vertices (0,0), (0,1), (1,1) and (1,0). Draw the image of the square under these tranformations. Then find the change in area of the square under these transformations.

a)
[1 1]
[1 2]

b)
[0 -1]
[2 -1]

c)
[4 1/4]
[3 1/3]
2. Homework Equations [/b]

The Attempt at a Solution

I've plotted out all of the matrices on a graph but i don't understand how to find the change in area. How do I find the change in area?

 

[Dick]

The vertices (0,0), (0,1), (1,1) and (1,0) make a square of area 1. If you plotted the image they map to you should get some kind of parallelogram in each case. You can use trig to find its area, but it's probably easiest if you know how the vector cross product is related to area.

 

[Cacophony]

Still not really getting it. I have been out of school for a while so I need a refresher on how to use trigonometry to find the change in area. What does change in area even mean in this case?

 

[Dick]

Still not really getting it. I have been out of school for a while so I need a refresher on how to use trigonometry to find the change in area. What does change in area even mean in this case?

You don't have to use trig if it's not fresh in you mind. Look at the vector cross product first. The cross product of two vectors is related to the area of the parallelogram that they span. Look it up.