Prove that \[ \left|\begin{array}{ccc} 1 & 1 & 1 \\ x & y & z \\ x^...

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If \( A=\left[\begin{array}{ccc}1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1\end{array}\right] \), then... If \( A=\left[\begin{array}{ccc}1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1\end{array}\right] \), then...
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If \(\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x &.... If \(\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x &....
If \( A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0\end{array}\right] \) and \... If \( A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0\end{array}\right] \) and \...
Consider matrices \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & 1 &... Consider matrices \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & 1 &...
\( \Delta_{1}=\left|\begin{array}{ccc}y^{5} z^{6}\left(z^{3}-y^{3}\right) & x^{4} z^{6}\left... \( \Delta_{1}=\left|\begin{array}{ccc}y^{5} z^{6}\left(z^{3}-y^{3}\right) & x^{4} z^{6}\left...
If \( \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1\end{array}\right]... If \( \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1\end{array}\right]...