Results 1 to 2 of 2

Thread: Standard Matrix Question

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    78

    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 $\displaystyle \left(\begin{array}{ccc}1&-2&0\\-2&-1&1\\0&0&-1\end{array}\right)$

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

    will the standard matrix be

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

    and

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

    Am I right with the above answers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    7
    Awards
    2
    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 $\displaystyle \theta_{1}$ and $\displaystyle \theta_{2},$ so that's what you'd better have.
    2. It's considered better practice to use non-italicized function names: $\displaystyle \cos(\theta)$ is better than $\displaystyle cos(\theta).$
    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: $\displaystyle \sin(\theta),$ etc.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Mar 10th 2011, 01:39 PM
  2. Standard matrix of T
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Aug 1st 2010, 09:39 PM
  3. Standard matrix problem, please help
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Sep 8th 2009, 04:59 AM
  4. What is the standard matrix?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Mar 30th 2009, 09:50 PM
  5. Finding standard matrix for T
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Jul 31st 2008, 11:30 AM

Search Tags


/mathhelpforum @mathhelpforum