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Math Help - Finding the Standard Matrix

  1. #1
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    Finding the Standard Matrix

    Could someone please explain how to find the standard matrix? I have a test tomorrow and my professor wasn't very clear about this part, and the textbook isn't helping much, either. Here are a couple of practice problems my professor gave us:

    Assume T is a linear transformation. Find the standard matrix of T.

    (1.) T: R^2 --> R^2 rotates points (about the origin) through -(pi)/4 radians (clockwise)

    (2.) T: R^2 --> R^2 is a vertical shear transformation that maps e1 into (e1 - 2(e2)) but leaves vector e2 unchanged.

    Any help would be greatly appreciated.
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  2. #2
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    Nevermind - I know how to do it now. I do have one question though. What does "vertical shear transformation" mean? Because it didn't really change the way I worked the problem.
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  3. #3
    MHF Contributor

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    The problem itself pretty much tells you what it is: T maps "e1 into (e1 - 2(e2)) but leaves vector e2 unchanged"- a "shear" stretches vectors along one axis.
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