Question

Prove that \begin{vmatrix} a & b &c \\ b & c &a \\ c &a & b \end{vmatrix} = (a+b+c)(ab+bc+ca-a^2-b^2-c^2)

18 Feb 2024
Answer :
Word Count : 155
To prove the determinant identity numerically, let's evaluate both sides for some chosen values of \( a, b, c \) and check if they are ____ _____ _____ __________ _____.
____ _____ ____ _______ _______ ______ ____ _______ ___ _________.
__________ ___ ___ _________ __________ ______ ________ ______ ___.
_____ _________ ____ _______ _____ _____.
__________ ______ ____ _________ ___ __________ ______ __________.
_______ _________ ___ ______ ___ ______.
___ ______ ____ _______ _________ _____ ____ _____ ____ __________ _________ _______.
___ _____ __________ __________ _______ ______ ____ ________ ________ ___ __________.
_________ ______ ___ __________ _________ _____ __________ ________ _________.
_______ ________ _______ ____ ________ _________ _______ ____ _______.
_________ __________ ___ ____ ________ ______ ______ ______.
__________ ____ __________ _______ _______.
_______ ____ _______ _________ _________ _________.
___ __________ ______ ___ _______.
________ __________ ________ ___ __________ ___ ____.
____ ________ ___ _______ _________ ________ ________ ______.
___ ________ __________ _______ ___.
____.
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