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Paragraph: For the system of linear equations 2 x+3 y+5 z=9,7 x+3 y-2 z=8 and 2 x+3 y+ z= Question: Under what condition does the above system of equations have infinitely many solutions?

Options

  1. A=5 and 9
  2. B=5 and =9
  3. C=9 and =5
  4. D=9 and 5

Correct answer

B. =5 and =9

Step-by-step solution

aligned & A= [ array ccc 2 & 3 & 5 7 & 3 & -2 2 & 3 & array ] and B= [ array l 9 8 array ] & ( Adj A)= [ array ccc 3 +6 & 15-3 & -21 -(7 +4) & 2 -10 & 39 15 & 0 & -15 array ] aligned For infinitely many solutions : ( Adj A) B=0 [ array c 27 +54+120-24 -21 -63 -36+16 -80+39 135+0-15 array ]= [ array l 0 0 0 array ] Hence, =9 and =5 .

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