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Manipal MET2014MathematicsDeterminants

The value of and for which the system of equations x+y+z=6, x+2 y+3 z=10 and x+2 y+ z= have no solution, are

Options

  1. A=3, 10
  2. B3, =10
  3. C3, 10
  4. DNone of these

Correct answer

A. =3, 10

Step-by-step solution

Given system of equation is aligned x+y+z & =6 x+2 y+3 z & =10 x+2 y+ z & = aligned If given system of equation has no solution, then D=0 and atleast one of the determinants D₁, D₂, D₃ 0 aligned & Here & aligned & D=0 & | array lll 1 & 1 & 1 1 & 2 & 3 1 & 2 & array |=0 aligned & 1(2 -6)-1( -3)+1(2-2)=0 & 2 -6- +3+0=0 & -3=0 & =3 aligned Also, D₁= | array ccc 6 & 1 & 1 10 & 2 & 3 & 2 & 3 array | 0 array rlrl & 6(6-6)-1(30-3 )+1(20-2 ) & 0 & 0-30+3 +20-2 0 & -10 0 & 10 array

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