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If the system of linear equations x+a...

If the system of linear equations `x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0` has a non zero solution then System is always non trivial solutions System is consistent only when `a=b=c` If `a!=b!=c` then `x=0,\ y=t ,\ z=-t\ AAt in R` If `a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R`

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ALLEN -DETERMINANTS-All Questions
  1. The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal...

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  2. An equilateral triangle has each of its sides of length 6 cm. If (x1, ...

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  3. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y...

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  4. Find the equation of the straight line parallel to Y - axis and at a d...

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  5. The determinant |[a^2, a^2-(b-c)^2,bc],[b^2,b^2-(c-a)^2,ca],[ c^2,c^2-...

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  6. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  7. Let f(x)=|1+sin^2x cos^2x4sin2xsin^2\ \ x1+cos^2x4sin2xsin^2xcos^2x1...

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  8. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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

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  10. Given that q^2-p r <0,\ p >0, then the value of {:|(p, q, px+qy), ...

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  11. If |{:(a, a, x), (m, m, m),(b, x, b):}|=0,\ then x may be equal to- ...

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  12. The value of the determinant {:|(alpha,beta,l), (alpha,x, n),(alpha,be...

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  13. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y...

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  14. If the system of equations x+y-3=0,\ (1+K)x+(2+K)y-8=0\ &\ x-(1+K)y...

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  15. If the determinant |[a+p, l+x, u+f], [b+q, x+y, v+g], [c+r, n+z, w+h]|...

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  16. The values of lambda for which the system of equations x+y+z=6,x+2y+3z...

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  17. If x , y , z are in A.P. , then the value of the determinant are in A....

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  18. Let p be the sum of all possible determinabnts of order 2 having 0,...

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  19. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  20. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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