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# A question about linear transformations... watch

1. Consider a shear linear transformation T in R^2 given by the matrix . Let "^" be a triangle with vertices at (-1,0), (1,0), and (0,1). What is the area of the triangle obtained from "^" if we apply the shear transformation six times in a row?

Can anybody help me with this?

2. There are two things you need to know here:

1. Areas are scaled by a factor of the determinant. So if is some shape with area and you apply your matrix , then the area of is .

2. The determinant of a power of a matrix is the power of the determinant of the matrix. That is,

You can take it from here
3. (Original post by nuodai)
There are two things you need to know here:

1. Areas are scaled by a factor of the determinant. So if is some shape with area and you apply your matrix , then the area of is .

2. The determinant of a power of a matrix is the power of the determinant of the matrix. That is,

You can take it from here

So is this how you solve it...

det(T) = = 1/2

(1/2)^6 = 1/64

The area of the triangle is...

(base)(height)(1/2) = (2)(1)(1/2) = 1

det(t) x area of the triangle = (1/64)(1) = 1/64...is this correct?
4. (Original post by Artus)
is this correct?
Yup that's fine

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