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The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ has

  1. A unique solution
  2. No solution
  3. An infinite number of solutions
  4. None of these
in Linear Algebra retagged by
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Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

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3 Answers

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Answer Unique Solution
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x + y + z = 6, 2x+ y +z = 7, x + 2 y +z = 8

              

1 1 1 6
2 1 1 7
1 2 1 8

we can also find it using Rank 

Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

rank[A] = rank[A|b] = 3 

hence unique solution

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Option a