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+5 votes

The equations.

  • $x_{1}+2x_{2}+3x_{3}=1$
  • $x_{1}+4x_{2}+9x_{3}=1$
  • $x_{1}+8x_{2}+27x_{3}=1$


  1. Only one solution.
  2. Two solutions.
  3. Infinitely many solutions.
  4. No solutions
asked in Linear Algebra by Veteran (42.8k points) | 208 views

1 Answer

+7 votes
Best answer
This is non homogeneous equation ...for such type of questions we have to check following 3 cases :

1)if rank(A)<rank(A|B) then AX=B has no solution

2)if rank(A|B)=rank(A)=no of unknowns then AX=B has unique non-zero solution

3)rank(A|B)=rank(A)<no of unknowns then infinite no of solution

here I'm getting rank(A|B)=rank(A)=no of unknowns =3 so only one solution..
answered by (329 points)
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hey how are you getting rank(A|B)=rank(A)??
Yes and the solution is (1,0,0).

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