# 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?

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7 years ago
#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
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#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?
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7 years ago
#4
(Original post by Artus)
is this correct?
Yup that's fine
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