1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the Standard Matrix A of a Linear Transformation T

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively.

    Find the standard matrix of T and determine whether T is one to one and if T is onto

    2. Relevant equations



    3. The attempt at a solution
    taking a 3x3 matrix entries [x1,x2,x3;x4,x5,x6] and multiply that by a 3x3 matrix with entries [1,1,0;1,0,1;0,1,1] and set that equal to a matrix with entries [1,0,3;1,1,4;1,3,0] and then got a system of equations from there by multiplying the left side out. And then set up an augmented matrix and used row reduction to find corresponding entries for A?
     
  2. jcsd
  3. Feb 2, 2013 #2
    If you call:


    [itex]
    V_1= \begin{pmatrix} 1\\1\\0\end{pmatrix},
    V_2= \begin{pmatrix} 1\\0\\1\end{pmatrix},
    V_3= \begin{pmatrix} 0\\1\\1\end{pmatrix}\\
    B_1=\begin{pmatrix} 1\\1\\1\end{pmatrix},
    B_2=\begin{pmatrix} 0\\1\\3\end{pmatrix},
    B_3=\begin{pmatrix} 3\\4\\0\end{pmatrix}
    [/itex]
    Then you may write that

    [itex]
    T\cdot\left ( V_1 V_2 V_3\right) = \left ( B_1 B_2 B_3 \right )
    [/itex]
    Observe a few things about [itex]\left ( V_1 V_2 V_3\right)[/itex] and you should be on your way to finding the solution.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the Standard Matrix A of a Linear Transformation T
Loading...