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Math Help - Matrix multiplication.

  1. #1
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    Matrix multiplication.

    to prove
    Η * Η’ = Η’ * Η

    Η= [a b]
    [c d]


    H'=[a' b']
    [c' d']
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Do the multiplication matrix and show us what you get!
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  3. #3
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    i Do the multiplication and i find a='a and d='d
    but my teacher say a’ = a b’ = c c’ = b and d’ = d
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  4. #4
    MHF Contributor Unknown008's Avatar
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    \left(\begin{array}{cc}a & b \\ c & d\end{array}\right) \cdot\left(\begin{array}{cc} a' & b' \\ c' & d'\end{array}\right) = \left(\begin{array}{cc}(aa'+bc') & (ab'+bd') \\(ca'+dc') & (cb' + dd')\end{array}\right)

    And

    \left(\begin{array}{cc} a' & b' \\ c' & d'\end{array}\right) \cdot \left(\begin{array}{cc}a & b \\ c & d\end{array}\right) = \left(\begin{array}{cc}(a'a+b'c) & (a'b+b'd) \\(c'a+d'c) & (c'b + d'd)\end{array}\right)


    Well, I'm not sure what you are trying to do, but your original post says prove that H.H' = H'.H

    Since we know that a = a', d = d', c = b' and b = c', then H.H' = H'.H is proved.
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  5. #5
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    we dont know that a = a', d = d', c = b' and b = c',
    we are trying to find that h*h'=h'*h
    and i think that the anser is a = a', d = d', c = b' and b = c',
    but i am not completely sure
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Well, for H.H' to be equal to H'.H, we must have a = a', d = d', c = b' and b = c'
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  7. #7
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    thnks dude!
    may the force be with you!!
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  8. #8
    MHF Contributor Unknown008's Avatar
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    Uh...okay...

    Thanks!
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  9. #9
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    sorry can you explain the answer plzzzzz??
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  10. #10
    MHF Contributor Unknown008's Avatar
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    You cannot prove that

    H.H' = H'H

    unless we know that a = a', d = d', c = b' and b = c'
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  11. #11
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    All you appear to have here is two unrelated matrices, H and H'.

    You cannot then prove that "H*H'= H'*H" because it is not true: matrix multiplication is not commutative.

    Or did you mean that H' is the transpose of H? No, that doesn't work either. So I don't know what you are asking.
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