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Math Help - Prove the identity

  1. #1
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    Prove the identity

    I don't understand this:

    Prove the identity without evaluating the determinants.


    \left|\begin{matrix}a_1&b_1&a_1+b_1+c_1\\a_2&b_2&a  _2+b_2+c_2\\a_3&b_3&a_3+b_3+c_3\end{matrix}\right|  =\left|\begin{matrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3  &b_3&c_3\end{matrix}\right|

    It's a question at the end of a section of properties of determinant functions, but I don't know how to do it
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  2. #2
    A Plied Mathematician
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    See here for a very similar thread. Columns versus rows makes little difference to a determinant.
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  3. #3
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    Thank you! I get it now.
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  4. #4
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    You're welcome. Have a good one!
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  5. #5
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    The determinant on the left is the sum of three determinants two of which have identical columns and are therefore zero.
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