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Math Help - Points transformed by a matrix.

  1. #1
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    [SOLVED]Points transformed by a matrix.

    So, my semester is ending in less than one week, and I've been studying for my Linear Algebra exam, but I can't seem to solve this problem.

    A, B, C -> 3 points [x, y];
    M -> a transformation Matrix.

    Demonstrate that if A, B and C are aligned, MA, MB and MC are also aligned.
    I.e : a line, defined by a 2*n matrix of points, will stay a line after being transformed by a matrix.


    If anyone could help me, I'd appreciate it, I've tried searching for a similar thread, but nothing came up. I hope it's clear enough

    Also, feel free to correct my English, the terminology i used might not be correct since it's directly translated from French.
    Last edited by Drav; December 16th 2010 at 12:47 PM. Reason: Solved
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  2. #2
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    Points A, B, C aligned means the difference vectors are parallel, i.e. A - B = k(B - C)

    Now, can you show that MA, MB, MC are aligned by using this? I.e. MA - MB = k'(MB - MC)

    Recall that a linear transformation has the property M(cA + c'B) = cMA + c'MB.
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  3. #3
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    Thanks, that's probably what I have to use. But I don't recall seeing this property (M(cA + c'B) = cMA + c'MB) in class, could you explain the meaning of c and c'?
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  4. #4
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    c and c' are just multiplicative constants (i.e. scalars / field elements).

    This property is actually at the heart of linear transformations and matrices. The only reason why matrix multiplications works the way it does is because of this property.
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