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  4. The system of equations x - 2y + 3z = 5, 2x- 2y + z = 0, -x + 2y - 3z = 6 has

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Q. The system of equations $x - 2y + 3z = 5, 2x- 2y + z = 0, -x + 2y - 3z = 6$ has

AP EAMCETAP EAMCET 2018

Solution:

Given system of equations,
$x-2 y+3 z=5$ ...(i)
$2 x-2 y+ z=0$ ...(ii)
$-x+2 y-3 z=6$ ...(iii)
$\because \Delta=\begin{vmatrix}1 & -2 & 3 \\ 2 & -2 & 1 \\ -1 & 2 & -3\end{vmatrix}$
$=1(6-2)+2(-6+1)+3(4-2)$
$=4-10+6=0$
$\Delta_{1}=\begin{vmatrix}5 & -2 & 3 \\ 0 & -2 & 1 \\ 6 & 2 & -3\end{vmatrix}$
$=5(6-2)+2(0-6)+3(0+12)$
$=20-12+36 \neq 0$
So, no solution.