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Math Help - Standard Matrix Question

  1. #1
    Junior Member
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    Standard Matrix Question

    1. Find the standard matrix defined by the linear transformation

    T(x,y,z) = (x-2y, -2x-y+z,-z)

    is it going to be \left(\begin{array}{ccc}1&-2&0\\-2&-1&1\\0&0&-1\end{array}\right)

    2. Let T_1 be the linear transformation corresponding to a rotation by an angle of \theta_1 about the x axis in R^3 and Let T_2 be the linear transformation corresponding to a rotation by an angle of \theta_2 about the z axis in R^3

    will the standard matrix be

    \left(\begin{array}{ccc}1&0&0\\0&cos \theta& -sin \theta\\0&sin  \theta&cos \theta\end{array}\right)

    and

    \left(\begin{array}{ccc}cos \theta&-sin \theta&0\\sin \theta&cost \theta& 0\\0&0&1\end{array}\right)

    Am I right with the above answers?
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  2. #2
    A Plied Mathematician
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    Your answers are close. For the rotations, I have several comments:

    1. Most important: your angles need to be subscripted. That is, the problem statement has \theta_{1} and \theta_{2}, so that's what you'd better have.
    2. It's considered better practice to use non-italicized function names: \cos(\theta) is better than cos(\theta).
    3. I would highly recommend ALWAYS putting parentheses around function arguments. I've been burned on that one before, and so rather than write in a way that people can understand, I would rather try to write in a way that no one can misunderstand. So I'd recommend writing trig functions this way: \sin(\theta), etc.
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