# Conditions for Linear transformation.

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This chapter starts as follows rotations about the origin and all reflections in lines through the origin can be expressed as functions with rules of the form

x ---> Ax

where A is a 2 x 2 matrix

any function with such a rule is called a linear transformation

a linear transformation of the plane is a function of the form

f: R^2 --> R^2

x---> Ax

the transformation f is said to be represented by the matrix A

note eigenvectors have not been studied

there is some problems beginning

for each of the following functions f : R^2 ----> R^2

either explain why f is not linear , or write down the matrix that represents f

a) f(x,y) = (x+2y,y-x)

b) f(x,y) = (x+y+2,y-2x)

c) f(x,y) = (2,-1)

d) f reflects the plane in the line x = 2

with answers

a) (1 2)

-1 1

c) not linear transformation because it maps (0,0) to (2,1)

How do you get these and the other answers what is the reasoning behind these

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