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    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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