- #1

- 168

- 0

Is there a formula to do this? The textbook just says to "reverse" the action of T to get T^-1 (T inverse). Can someone explain to me in laymen terms, how to accomplish this? For example,

For T = [2x y]^T is T^-1 = [-2x y]^T?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter KataKoniK
- Start date

- #1

- 168

- 0

Is there a formula to do this? The textbook just says to "reverse" the action of T to get T^-1 (T inverse). Can someone explain to me in laymen terms, how to accomplish this? For example,

For T = [2x y]^T is T^-1 = [-2x y]^T?

- #2

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,950

- 19

- #4

- 168

- 0

To make my question more clear, in the following example, how come x + 5y becomes x - 5y? The question basically says to *let T be the transformation induced by an invertible 2x2 matrix A. In each case, interpret T^-1 geometrically*. For this question,

A = 1 5

0 1

http://img332.imageshack.us/img332/7757/ex3re.jpg [Broken]

Also, just to note that in my initial post, the matrix A for that one was

A = 2 0

0 1

A = 1 5

0 1

http://img332.imageshack.us/img332/7757/ex3re.jpg [Broken]

Also, just to note that in my initial post, the matrix A for that one was

A = 2 0

0 1

Last edited by a moderator:

- #5

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,950

- 19

You could, of course, verify it by turning the crank: check that T T

- #6

- 168

- 0

Hurkyl said:

You could, of course, verify it by turning the crank: check that T T^{-1}is the identity.

Dumb question, but how do we get the identity by doing T T

- #7

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,950

- 19

(Or equivalently, multiplying their matrix representations)

Technically, you should prove both T T^-1 and T^-1 T are both the identity.

- #8

- 168

- 0

Alright, thanks.

Share: