GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
173 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 (29.5k points)   | 173 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 May 2017
  1. akash.dinkar12

    3578 Points

  2. pawan kumarln

    2314 Points

  3. Bikram

    1950 Points

  4. Arjun

    1852 Points

  5. sh!va

    1682 Points

  6. Debashish Deka

    1296 Points

  7. Devshree Dubey

    1282 Points

  8. Arunav Khare

    1122 Points

  9. Angkit

    1072 Points

  10. LeenSharma

    1028 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 29 - Jun 04
  1. Arunav Khare

    246 Points

  2. Arjun

    202 Points

  3. pawan kumarln

    108 Points

  4. Rupendra Choudhary

    94 Points

  5. Niharika 1

    90 Points


22,909 questions
29,243 answers
65,403 comments
27,745 users