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Math Help - Linear algebra Matrices

  1. #1
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    Linear algebra Matrices

    Let T: \Re^2 \rightarrow \Re^2 be the map that first projects points on to the line  x_2=\sqrt {3}x_1 than rotates 30 degrees clockwise.

    a) Find the matrix representation of T.
    b) Find the range of T (describe it).
    c) Find the nullset of T (describe it).

    Sorry for posting so many problems. I'm new to this subject and I'm confused.
    Thank you!
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  2. #2
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    Quote Originally Posted by Linnus View Post
    Let T: \Re^2 \rightarrow \Re^2 be the map that first projects points on to the line  x_2=\sqrt {3}x_1 than rotates 30 degrees clockwise.

    a) Find the matrix representation of T.
    b) Find the range of T (describe it).
    c) Find the nullset of T (describe it).

    Sorry for posting so many problems. I'm new to this subject and I'm confused.
    Thank you!
    The matrix for rotation is A=\left[ \begin{array}{cc}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right].

    The matrix for dilations is B = \left[\begin{array}{cc} \sqrt{3} & 0 \\ 0 & \sqrt{3} \end{array} \right].

    Thus, what you are looking for is the matrix product AB.
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