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Prove that |a a x m m m b x b|=m(x-a)(x-...

Prove that `|a a x m m m b x b|=m(x-a)(x-b)`

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ALLEN-DETERMINANTS-All Questions
  1. Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a...

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  2. If |3^2+k4^2 3^2+3+k4^2+k5^2 4^2+4+k5^2+k6^2 5^2+5+k|=0 then the value...

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  3. Prove that |a a x m m m b x b|=m(x-a)(x-b)

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  4. Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2d...

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  5. Find the nature of solution for the given system of equation: x+2y+3...

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  6. If the following equations x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0...

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  7. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

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  8. If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=...

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  9. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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  10. If p x^4\ \ q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x|t h ...

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  11. For positive numbers x ,\ y\ a n d\ z the numerical value of the deter...

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  12. For a non-/cro real a,b and c |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,...

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  13. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

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  14. Let a determinant is given by A=|[a,b,c],[p,q,r],[x,y,z]| and suppose ...

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  15. If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 t...

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  16. If f(x)=|1xx+1 2xx(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500...

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  17. The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal...

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

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  19. If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y + z =...

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  20. If f^(prime)(x)=|m x m x-p m x+p nn+p n-p m x+2n m x+2n+p m x+2n-p| , ...

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