GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
155 views

The equations.

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

have

  1. Only one solution.
  2. Two solutions.
  3. Infinitely many solutions.
  4. No solutions
asked in Linear Algebra by Veteran (29k points)   | 155 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)  
selected by
hey how are you getting rank(A|B)=rank(A)??
Top Users Feb 2017
  1. Arjun

    4704 Points

  2. Bikram

    4004 Points

  3. Habibkhan

    3738 Points

  4. Aboveallplayer

    2966 Points

  5. sriv_shubham

    2278 Points

  6. Smriti012

    2212 Points

  7. Arnabi

    1814 Points

  8. Debashish Deka

    1788 Points

  9. sh!va

    1444 Points

  10. mcjoshi

    1444 Points

Monthly Topper: Rs. 500 gift card

20,788 questions
25,938 answers
59,535 comments
21,929 users