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Math Help - trying to figure out how to prove two matrices are equal

  1. #1
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    trying to figure out how to prove two matrices are equal

    Ok, so I am trying to prove that one matrix equals another without finding determinates. The first matrix is
    (1, a, bc)
    (1, b, ac)
    (1, c, ab)

    I need to figure out how to make that equal to:
    (1, a, a^2)
    (1, b, b^2)
    (1, c, c^2)

    I need to do this using column operations, so far I've tried multiplying the 2nd column by abc and subtracting the 3rd column to get the 3rd column, but I can't figure out how to finish off and get the squared letters by themeselves...

    Thanks to anyone who takes time to figure this out, it's a big help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by snoboarder2k6 View Post
    Ok, so I am trying to prove that one matrix equals another without finding determinates. The first matrix is
    (1, a, bc)
    (1, b, ac)
    (1, c, ab)

    I need to figure out how to make that equal to:
    (1, a, a^2)
    (1, b, b^2)
    (1, c, c^2)

    I need to do this using column operations, so far I've tried multiplying the 2nd column by abc and subtracting the 3rd column to get the 3rd column, but I can't figure out how to finish off and get the squared letters by themeselves...

    Thanks to anyone who takes time to figure this out, it's a big help
    two matrices are equal if their corresponding entries are equal
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  3. #3
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    well, yeah, but not knowing the values of a, b, and c, you can't just say bc = a^2 etc.

    thanks though
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by snoboarder2k6 View Post
    well, yeah, but not knowing the values of a, b, and c, you can't just say bc = a^2 etc.

    thanks though
    well, a = b = c works...

    can you not state that as a solution?
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  5. #5
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    true, but the object of the problem is to prove that the first matrix equals the second matrix generally, not just by stating one particular case.
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