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\( \left|\begin{array}{lll}1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3}\end{array}\right|=(a-... \( \left|\begin{array}{lll}1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3}\end{array}\right|=(a-...
Prove that \( \left|\begin{array}{lll}b+c & a-b & a \\ c+a & b-c & b \\ a+b & c-a & c\end{array}... Prove that \( \left|\begin{array}{lll}b+c & a-b & a \\ c+a & b-c & b \\ a+b & c-a & c\end{array}...
If \( \Delta=\left|\begin{array}{ccc}0 & b-a & c-a \\ a-b & 0 & c-b \\ a-c & b-c & 0\end{array}\.... If \( \Delta=\left|\begin{array}{ccc}0 & b-a & c-a \\ a-b & 0 & c-b \\ a-c & b-c & 0\end{array}\....
\( \left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ c a & c b & c^{2}+1\end... \( \left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ c a & c b & c^{2}+1\end...
Let \( D_{1}=\left|\begin{array}{ccc}a & b & a+b \\ c & d & c+d \\ a & b & a-b\end{array}\right|.... Let \( D_{1}=\left|\begin{array}{ccc}a & b & a+b \\ c & d & c+d \\ a & b & a-b\end{array}\right|....
If \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \) (where \( b c \neq 0 \) ) sat.... If \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \) (where \( b c \neq 0 \) ) sat....
If \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & .... If \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & ....
\[ \left|\begin{array}{ccc} b+c & a & a \\ b & c+a & b \\ c & c & a... \[ \left|\begin{array}{ccc} b+c & a & a \\ b & c+a & b \\ c & c & a...