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If the system of equation aligned & 2 x+ y+3 z=5 & 3 x+2 y-z=7 & 4 x+5 y+ z=9 aligned has infinitely many solutions, then ( ^2+ ^2 ) is equal to :

Options

  1. A22
  2. B18
  3. C26
  4. D30

Correct answer

C. 26

Step-by-step solution

=0 | array ccc 2 & & 3 3 & 2 & -1 4 & 5 & array |=0 2(2 +5)+ (-4-3 )+3(7)=0 4 -3 -4 +31=0 ...(1) aligned & ₃=0 | array lll 2 & & 5 3 & 2 & 7 4 & 5 & 9 array |=0 & 2(-17)+ (1)+5(7)=0 & =-1 aligned from equation (1) 4 +3 +4+31=0 =-5 ^2+ ^2=26

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