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If the system of equation ax+y+z=0, x+by...

If the system of equation `ax+y+z=0, x+by+z=0, x+y+cz=0,(a,b,c!=1)` has non trivial solution (non -zero solution) then`1/(1-a)+1/(1-b)+1/(1-c)=`

A

1

B

`-1`

C

2

D

2

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The correct Answer is:
A
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AAKASH SERIES-MATRICES -LINEAR EQUATIONS - EXERCISE - II
  1. If the system of equation ax+y+z=0, x+by+z=0, x+y+cz=0,(a,b,c!=1) has ...

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  2. The system of equations (sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0...

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  3. The equation x+y+z=6, x+2y+3z=10, x+2y+lamdaz=mu have unique solution ...

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  4. The system of linear equations x+y+z=2, 2x+y-z=3, 3x+2y+kz=4 has a uni...

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  5. If the system of equations x+2y+3z=lamdax,3x+y+2z=lamday,2x+3y+z=lamda...

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  6. By eliminating a,b,c from the Homogeneous Equations x=(a)/(b-c),y=(b)/...

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  7. The system of equations x+y+z=6, x+2y+3z=10,x+2y+lamdaz=mu is inconsis...

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  8. The rank of [(1,-1,1,1),(-1,1,1,2),(1,1,-1,3)] is

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  9. If a,b,c are all different and the equations ax+a^(2)y+(a^(3)+1)z=0, b...

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  10. The values of lamda for which the system of equations x+y-3=0, (1+ lam...

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  11. The system of equations -2x+y+z=a,x-2y+z=b,x+y-2z=c is consistent if

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  12. The system of equations -2x+y+z=a,x-2y+z=b,x+y-2z=c is consistent if

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  13. The rank of [(1,0,2),(0,1,-2),(1,-1,4),(2,2,8)] is

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  14. If the matrix A=[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is of ra...

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  15. The rank of the matrix [(-1,2,5),(2,-4,a-4),(1,-2,a+1)] is

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  16. If the system of equations (k+1)^(3)x+(k+2)^(3)y=(k+3)^(2),(k+1)x+(k+2...

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  17. Statement - I The soluton of the system of equations 2x-y+3z=9,x+y+z=...

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  18. Statement I : Rank of a matrix is defined for only square matrices ...

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  19. Match the following from List - I to List - II {:(,"List - I",,"List...

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  20. the system of equations x+y+z=4,2x+5y-2z=3,x+7y-7z=5 has no solution.

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