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Math Help - Prove that the determinants are equal

  1. #1
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    Prove that the determinants are equal

    b+c-a a a a b c
    b c+a-b b = b c a
    c c a+b-c c a b
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  2. #2
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    Quote Originally Posted by sunitaparija View Post
    b+c-a a a a b c
    b c+a-b b = b c a
    c c a+b-c c a b
    The brute force approach:

    Calculate \left| \begin{array}{ccc}<br />
b + c - a & a & a \\<br />
b & c + a - b & b \\<br />
c & c & a + b - c \end{array} \right|.

    Calculate \left| \begin{array}{ccc}<br />
a & b & c \\<br />
b & c & a \\<br />
c & a & b \end{array} \right|.


    Alternatively, you could do row operations on \left| \begin{array}{ccc}<br />
a & b & c \\<br />
b & c & a \\<br />
c & a & b \end{array} \right|.
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  3. #3
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    The Determinant sum has to be proved without expanding.
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