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If a,b,c are all different and the equat...

If a,b,c are all different and the equations `ax+a^(2)y+(a^(3)+1)z=0, bx+b^(2)y+(b^(3)+1)z=0, cx+c^(2)y+(c^(3)+1)z=0` have a nonzero solution , then

A

`-1`

B

1

C

`a+b+c`

D

0

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-MATRICES -LINEAR EQUATIONS - EXERCISE - II
  1. The equation x+y+z=6, x+2y+3z=10, x+2y+lamdaz=mu have unique solution ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Consider the system of equations ax + by + cz = 2 bx + cy + az = 2...

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  20. The equation x-y+2z=4,3x+y+4z=6, x+y+z=1 have

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