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Math Help - determinant

  1. #1
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    determinant

    prove that LHS=RHS without evaluating the determinant

    l a1+b1t a2+b2t a3+b3t l= l a1 a2 a3 l
    l a1t+b1 a2t+b2 a3t+b3 l= (1-t^2) l b1 b2 b3 l
    l c1 c2 c3 l= l c1 c2 c3 l
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    prove that LHS=RHS without evaluating the determinant

    l a1+b1t a2+b2t a3+b3t l= l a1 a2 a3 l
    l a1t+b1 a2t+b2 a3t+b3 l= (1-t^2) l b1 b2 b3 l
    l c1 c2 c3 l= l c1 c2 c3 l
    This is nearly impossible to read.

    Are you trying to prove that this is true?

    \left|\begin{matrix}a_1 + b_1t & a_2 + b_2t & a_3 + b_3t \\ a_1t + b_1 & a_2t + b_2 & a_3t + b_3 \\ c_1 & c_2 & c_3\end{matrix}\right| = (1 - t^2)\left|\begin{matrix}a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{matrix}\right|
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  3. #3
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    yes(:
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