Matrix and Determinant
79464
Solutions of the equation \(p+1 p+1 p+x=0\) are
1 \(x=1,2\)
\(\begin{array}{lll}3 & x+1 & x+2\end{array}\)
2 \(x=2,3\)
3 \(\mathrm{x}=1, \mathrm{p}, 2\)
4 \(\mathrm{x}=1,2,-\mathrm{p}\)
Explanation:
(A) : Given,
\(\left|\begin{array}{ccc} 1 & 1 & x \\ p+1 & p+1 & p+x \\ 3 & x+1 & x+2 \end{array}\right|=0\)
\(\mathrm{R}_{2} \rightarrow R_{2}-R_{1}\)
\(\left|\begin{array}{ccc} 1 & 1 & x \\ p & p & p \\ 3 & x+1 & x+2 \end{array}\right|=0\)
\(\mathrm{p}\left|\begin{array}{ccc} 1 & 1 & \mathrm{x} \\ 1 & 1 & 1 \\ 3 & \mathrm{x}+1 & \mathrm{x}+2 \end{array}\right|=0\)
\(\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-\mathrm{R}_{1}\)
\(\mathrm{C}_{1} \rightarrow \mathrm{C}_{1}-\mathrm{C}_{2}\left|\begin{array}{lll}1 & 1 & \mathrm{x} \\ 1 & 1 & 1 \\ 2 & \mathrm{x} & 2\end{array}\right|=0\)
\(\mathrm{p}\left|\begin{array}{ccc}0 & 1 & \mathrm{x} \\ 0 & 1 & 1 \\ 2-\mathrm{x} & \mathrm{x} & 2\end{array}\right|=0\)
\(\mathrm{p}(2-\mathrm{x})\left|\begin{array}{ll}
1 & \mathrm{x} \\ 1 & 1 \end{array}\right|=0\)
\(\mathrm{p}(2-\mathrm{x})(1-\mathrm{x})=0\)
\(\mathrm{x}=1,2\)
