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

The system of equations $x-2 y+3 z=5$, $2 x-2 y+z=0,-x+2 y-3 z=6$ has
  1. infinitely many solutions
  2. exactly two solutions
  3. unique solution
  4. no solution

Solution

Given system of equations,
$ \begin{aligned} \because \Delta & =\left|\begin{array}{ccc} 1 & -2 & 3 \\ 2 & -2 & 1 \\ -1 & 2 & -3 \end{array}\right|=1(6-2)+2(-6+1)+3(4-2) \\ & =4-10+6=0 \\ \Delta_1 & =\left|\begin{array}{ccc} 5 & -2 & 3 \\ 0 & -2 & 1 \\ 6 & 2 & -3 \end{array}\right|=5(6-2)+2(0-6)+3(0+12) \\ & =20-12+36 \neq 0 \end{aligned} $ So, no solution

Asked in: AP EAMCET 2018 (22 Apr Shift 2)

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