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Math Help - Linear Transfrm. Projection Problem

  1. #1
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    Linear Transfrm. Projection Problem

    Let T: R^2->R^2. Include figures for each of the following parts.
    a) Find a formula T(a,b) where T represents the projectionon the y-axis along x-axis

    My Solution, (CAN SOMEONE SEE IF THIS IS RIGHT):

    R(T) = Y-AXIS
    N(T) = X-AXIS
    T(x,y) = (0,y)

    b) find a formula T(a,b) where T represents the projectin on the y-axis along the line L = {(s,s): s is in R}.
    solution
    T(s,y) = ( s, s)
    R(T) = R^2
    N(T) = {0}

    is this right?
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  2. #2
    Super Member Rebesques's Avatar
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    For the second, R(T)=L.
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  3. #3
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    Quote Originally Posted by ruprotein View Post
    Let T: R^2->R^2. Include figures for each of the following parts.

    b) find a formula T(a,b) where T represents the projectin on the y-axis along the line L = {(s,s): s is in R}.
    solution
    T(s,y) = ( s, s)
    R(T) = R^2
    N(T) = {0}

    is this right?
    Quote Originally Posted by Rebesques View Post
    For the second, R(T)=L.
    A projection along L onto the y-axis means L is the null space and the y-axis is the range. See this.
    So

    T(a,b) = (0,b-a)
    R(T) = y-axis
    N(T) = L

    <br />
\setlength{\unitlength}{.7cm}<br />
\begin{picture}(4,4)<br /> <br />
\qbezier(-1,-1)(-1,-1)(4,4)<br />
\qbezier(2,3)(2,3)(0,1)<br />
\put(1.8,3.3){$(a,b)$}<br />
\put(-2,1){$T(a,b)$}<br />
\put(1.3,.8){$L$}<br /> <br />
\qbezier(0,0)(0,0)(4,0)<br />
\qbezier(0,-2)(0,-2)(0,4)<br /> <br />
\end{picture}<br />


    PS: I think the answer to problem (a) is correct.
    Last edited by JakeD; August 24th 2007 at 10:48 AM.
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  4. #4
    Super Member Rebesques's Avatar
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    Yeah I guess you 're right. The way I read it I thought it was the other way round.
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