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AP EAMCET202124 Aug 2021Morning ShiftMathematicsDeterminantsActual

The system of equations 2 x+6 y=-11 , 6 x+20 y-6 z=-3 and 6 y-18 z=-1 are

Options

  1. Ainconsistent
  2. Bconsistent with unique solution
  3. Cconsistent with countable infinite mary solutions
  4. Dconsistent with infinitely many solutions

Correct answer

A. inconsistent

Step-by-step solution

gathered Given, 2 x+6 y=-11 6 x+20 y-6 z=-3 6 y-18 z=-1 gathered Using Cramer's rule, aligned & D= | array ccc 2 & 6 & 0 6 & 20 & -6 0 & 6 & -18 array | & =2(20 (-18)-6 (-6)-6(6 (-18)-(-6) 0) & =2(-360+36)-6(-108) & =2(-360+36)-6(-108) & =2(-324)+648 & =-648+648=0 & D₁= | array ccc -11 & 6 & 0 -3 & 20 & -6 -1 & 6 & -18 array |=-11(-324)-6(54-6) & =-3564-6(48) & =-3564-288=-3852 0 & D₂= | array ccc 2 & -11 & 0 6 & -3 & -6 0 & -1 & -18 array |=2(54-6)+11(-108) & =2(48)+(-1188)=96-1188=-1092 0 & D₃= | array ccc 2 & 6

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