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The system of linear equations x+2 y+z=4,2 x+4 y+2 z=8 and 3 x+6 y+3 z=10 has

Options

  1. Aa unique solution
  2. Binfinite many solutions
  3. Cno solution
  4. Dexactly three solutions

Correct answer

B. infinite many solutions

Step-by-step solution

x+2 y+z=42 x+4 y+2 z=83 x+6 y+3 z=10D= | array lll 1 & 2 & 1 2 & 4 & 2 3 & 6 & 3 array |=0D₁= | array ccc 4 & 2 & 1 8 & 4 & 2 10 & 6 & 3 array |=0D₂= | array ccc 1 & 4 & 1 2 & 8 & 2 3 & 10 & 3 array |=0D₃= | array ccc 1 & 2 & 4 2 & 4 & 8 3 & 6 & 10 array |=0 D=D₁=D₂=D₃=0 System has infinite solutions.

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