# TIFR2010-Maths-B-14

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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

edited

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..

selected
0
hey how are you getting rank(A|B)=rank(A)??
0
Yes and the solution is (1,0,0).

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