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Prove that the system of equations in x...

Prove that the system of equations in `xa +y+z=0 ` , ` x +by +z=0 ` , ` x +y+cz=0 ` has a non - trivial solution then `1/(1-a) + 1/(1-b)+ 1/(1-c)=`

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ALLEN-DETERMINANTS-All Questions
  1. If ∣ x - 2 -3 3x 2x ∣ =3, find the negative of integer va...

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  2. If x,y and y are not all zero and if ax+by+cz=0,bx+cy+az=0 and cx...

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  3. Prove that the system of equations in xa +y+z=0 , x +by +z=0 ,...

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  4. If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1...

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  5. The value of |alpha| for which the system of equation alphax+y+z=alpha...

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  6. If D=|(1, 1, 1), (1, 1+x, 1), (1, 1, 1+y)| for x!=0, y!=0 then D is (...

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  7. Let a, b, c be any real numbers. Suppose that there are real number...

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  8. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  9. Consider the system of linear equations; x-1\ +2x2+x3=3, 2x1+3x2+3=3, ...

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  10. The number of value of k for which the linear equations 4x+k y+2z=0k x...

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  11. If the trivial solution is the only solution of the system of equation...

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  12. The number of values of k for which the system of equations (k+1)x+8y=...

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  13. If a ,b ,c are sides of a scalene triangle, then value of |[a, b, c] ,...

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  14. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

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  15. Assertion : The system of linear equations x+(sinalpha)y+(cosalpha)z=0...

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  16. Consider the system of equations x+a y=0,\ y+a z=0.\ Then the set of ...

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  17. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

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  18. The set of all values of lamda for which the system of linear equation...

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  19. The system of linear equations x+lambday -z=0 lambdax -y-z=0 ...

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  20. The number of distinct real roots of the equation |{:(cosx, sinx, sinx...

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