Question

Дана матрица
|1 1 1|
|1 1-х 1| =0
|1 1 2-х|
Равно нулю, найдите решение

Answer 1

Ответ:

$\left|\begin{array}{ccc}1&1&1\\1&1-x&1\\1&1&2-x\end{array}\right|=0\\\\\\\Big((1-x)(2-x)-1\Big)-\Big((2-x)-1\Big)+(1-(1-x)\Big)=0\\\\2-3x+x^2-1-1+x+x=0\\\\x^2-x=0\\\\x(x-1)=0\\\\\boxed{\ x_1=0\ ,\ x_2=1\ }$

$P.S.\ \ \left|\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right|=a_{11}\cdot A_{11}+a_{12}\cdot A_{12}+a_{13}\cdot A_{13}$

$A_{11}=\left|\begin{array}{ccc}a_{22}&a_{23}\\a_{32}&a_{33}\end{array}\right|=a_{22}\, a_{33}-a_{23}\, a_{32}\\\\A_{12}=-\left|\begin{array}{ccc}a_{21}&a_{23}\\a_{31}&a_{33}\end{array}\right|=-(a_{21}\, a_{33}-a_{23}\, a_{31})\\\\A_{13}=\left|\begin{array}{ccc}a_{21}&a_{22}\\a_{31}&a_{32}\end{array}\right|=a_{21}\, a_{32}-a_{22}\, a_{31}$