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Math Help - linear transformation

  1. #1
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    linear transformation

    getting ready for final need some help
    (1) 1
    Question: R squared through R cubed is a linear transformation.if T(1)= (1),
    1 1
    T(1 = (0) find T(2)
    -1) 1 (4)

    have no idea
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  2. #2
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    Opalg's Avatar
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    Quote Originally Posted by fatboy View Post
    getting ready for final need some help
    (1) 1
    Question: R squared through R cubed is a linear transformation.if T(1)= (1),
    1 1
    T(1 = (0) find T(2)
    -1) 1 (4)

    have no idea
    This is completely illegible as it stands. I think you mean something like "If T\begin{bmatrix}1\\1\end{bmatrix} = \begin{bmatrix}?\\?\\?\end{bmatrix} and T\begin{bmatrix}1\\-1\end{bmatrix} = \begin{bmatrix}?\\?\\?\end{bmatrix}, find T\begin{bmatrix}2\\4\end{bmatrix}."

    I suggest you repeat the problem, writing the vectors as rows rather than columns. This will be a lot easier to read.
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  3. #3
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    yea sorry about that i dont know how to write like that on my computer, but the way you did it is the right question. the first row is 1,1,1 and the second is 1,0,1 is the question marks you put in.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by fatboy View Post
    yea sorry about that i dont know how to write like that on my computer, but the way you did it is the right question. the first row is 1,1,1 and the second is 1,0,1 is the question marks you put in.
    <br />
T\begin{bmatrix}1\\1\end{bmatrix} = \begin{bmatrix}1\\1\\1\end{bmatrix}

    <br />
T\begin{bmatrix}1\\-1\end{bmatrix} = \begin{bmatrix}1\\0\\1\end{bmatrix}

    we need to solve a(1,1)+b(1,-1)=(x,y)

    This gives the system

    a+b=x
    a-b=y

    Solving gives

    a=\frac{x+y}{2}, \mbox{ and } b=\frac{x-y}{2}

    Now using the linear property of transforms on a(1,1)+b(1,-1)=(x,y) we get

    T(x,y)=T[a(1,1)+b(1,-1)]=T[a(1,1)]+T[b(1,-1)]=aT(1,1)+bT(1,-1)

    T(x,y)=a(1,1,1)+b(1,0,1)=\left(\frac{x+y}{2},\frac  {x+y}{2},\frac{x+y}{2} \right)+\left( \frac{x-y}{2},0,\frac{x-y}{2}\right)

    T(x,y)=\left( x, \frac{x+y}{2},x\right)

    Now we can use this to find T(2,4)

    T(2,4)=\left( 2, \frac{2+4}{2},2\right)=(2,3,2)
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  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Here is the link to the La Tex help forum

    http://www.mathhelpforum.com/math-help/latex-help/

    Here is a link to a few different sites with code

    http://amath.colorado.edu/documentat...eX/Symbols.pdf


    http://en.wikipedia.org/wiki/Help Formula

    You can also look at other code by double clicking on it, or just hoover your mouse over the code.
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