determinant
Posted: Tue Mar 09, 2010 8:04 pm
\( a, b, c, d \in C. \)Aratati ca
\( \det \begin{pmatrix} b + c + d & a & a & a \\
b & a + c + d & b & b \\
c & c & a + b + d & c \\
d & d & d & a + b + c \\
\end{pmatrix} = 4\sum abc(a + b + c) \)
\( \det \begin{pmatrix} b + c + d & a & a & a \\
b & a + c + d & b & b \\
c & c & a + b + d & c \\
d & d & d & a + b + c \\
\end{pmatrix} = 4\sum abc(a + b + c) \)