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Math Help - Matrices

  1. #1
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    Matrices

    This isn't statistics, but I can't find a Matrices section in the forum...and my teacher combined statistics with matrices at school, so hopefully someone can help me out with this problem!

    A matrix X satisfies the equation PX=Y, where P (2 by 2) = 1 3, 2 6 and Y (2 by 1) = 5, 10.
    a) show that in the case when X (2 by 1) = 2, 1, the equation PX=Y is satisfied.
    b) in the case when X (2 by 1) = 8, k, the equation is also satisfied. Find the value of k.
    c) i- Calculate P (2 by 1) = (3t, -t), where t is any real number.
    ii- Hence or otherwise show that if X (2 by 1) = (2, 1) + t(3, -1), then the equation PX=Y is always satisfied.

    I figured out a) and b), i only need help with c). But I put a) and b) here for the sake of knowing the whole question to answer c) for whoever is going to do this. Please show full soluions, thank you!!!
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  2. #2
    Member mabruka's Avatar
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    What do you mean with P(2 by 1) ??


    Is that a vector with 2 rows and 1 column?



    If it is then there is no way P.X is defined with X being a 2 row 1 column vector.


    2x1 2x1 is not defined.
    P must be always a 2x2 matrix like in a and b.


    Please explain better what do you mean for question c).
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  3. #3
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    P is a 2 by 1 matrix.
    The first row is 3t and the second row is -t.
    I have to find what t is.

    Then I have to show that if X = 2, 1 (a 2 by 1 matrix where the first row is 2 and the second row is 1) + t(3, -1) -->a 2 by 1 matrix where 3 is the first row and -1 is the second row, then the equation +X=Y is always satisfied.

    I bolded the question because my descibing of it makes it look confusing!
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  4. #4
    Member mabruka's Avatar
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    but number c)

    Calculate P, where P =(3t, -t) t real number.

    Just that?


    Something is missing UNLESS you are asked to PLOT P. In that case P is a line that passes through the origin int he direction of vector (3,-1).
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