How to determine change in area of matrices tranformations.

Click For Summary

Homework Help Overview

The discussion revolves around understanding the effects of matrix transformations on a square defined by specific vertices and determining the change in area resulting from these transformations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the initial problem of transforming a square using given matrices and express confusion about calculating the change in area. There are mentions of using trigonometry and the vector cross product as potential methods for finding the area of the transformed shapes.

Discussion Status

Some participants are exploring different methods to understand the change in area, with references to trigonometry and vector cross products. There is a recognition of the need for clarification on these concepts, but no consensus has been reached on a specific approach.

Contextual Notes

Participants indicate a lack of recent experience with the relevant mathematical concepts, which may be affecting their understanding of the problem. There is also a mention of the original area of the square being 1, which may serve as a reference point for discussing changes in area.

Cacophony
Messages
41
Reaction score
0

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?
 
Last edited:
Physics news on Phys.org
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.
 
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?
 
Cacophony said:
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.
 

Similar threads

Replies
23
Views
5K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
7
Views
4K
  • · Replies 40 ·
2
Replies
40
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 11 ·
Replies
11
Views
5K
Replies
15
Views
4K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K