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Math Help - Prob not real tough, but having troubles...

  1. #1
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    Prob not real tough, but having troubles...

    Hey guys, I'm new to this forum so Hi to everyone. I have a few problems that I"m really having trouble with...I'll start with this one hopefully you guys can help me out.
    I want to find an A mxn matrix such that f is linear:
    Ax = F(x)

    And what I've done:
    Suppose:
    (a11 a12) * x1 = f1(x)

    (a21 a22) * x2 = f2(x)
    (This is supposed to be Ax = b) a 2x2 times a 1x2 i just dont kno how to make matrices here)

    x1 and x2 can be anything so set x2 = 0
    get:
    a11*x1 = f1(x1)

    a21*x1 = f1(x1)

    My professor recommends I now solve for a11, a21 and then the others to construct the A matrix so that f is linear. I have no idea what to do! He says f(x1) can't be anything because it needs to be linear. Please help!
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by exostratics View Post
    Hey guys, I'm new to this forum so Hi to everyone. I have a few problems that I"m really having trouble with...I'll start with this one hopefully you guys can help me out.
    I want to find an A mxn matrix such that f is linear:
    Ax = F(x)

    And what I've done:
    Suppose:
    (a11 a12) * x1 = f1(x)

    (a21 a22) * x2 = f2(x)
    (This is supposed to be Ax = b) a 2x2 times a 1x2 i just dont kno how to make matrices here)

    x1 and x2 can be anything so set x2 = 0
    get:
    a11*x1 = f1(x1)

    a21*x1 = f1(x1)

    My professor recommends I now solve for a11, a21 and then the others to construct the A matrix so that f is linear. I have no idea what to do! He says f(x1) can't be anything because it needs to be linear. Please help!
    Edit/Delete Message
    Wouldnt that happen for any m x n matrix?

    For any m x n matrix A,isnt the map x \rightarrow Ax (where x is a column vector) a linear map?
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  3. #3
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    I don't know...

    I don't know, but I do know he wants me to specifically solve out for the A matrix.
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  4. #4
    Lord of certain Rings
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    Quote Originally Posted by exostratics View Post
    I don't know, but I do know he wants me to specifically solve out for the A matrix.

    You should be more clear. If x is a column vector(n x 1), then for any m x n matrix A, F(x) = Ax is a linear map.

    Proof:
    Vector Addition: F(x1) + F(x2) = Ax1 + Ax2 = A(x1 + x2) = F(x1+x2).
    Scalar Multiplication: F(ax) = A(ax) = a(Ax) = aF(x).

    Thus F is a linear map.
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