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If a+b+c=0, one root of |a-x c b c b-x a...

If `a+b+c=0,` one root of `|a-x c b c b-x a b a c-x|=0` is `x=1` b. `x=2` c. `x=a^2+b^2+c^2` d. `x=0`

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ALLEN-DETERMINANTS-All Questions
  1. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2) .

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  2. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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  3. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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  4. Prove that |b+c a a b c...

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  5. about to only mathematics

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  6. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  7. If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

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  8. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

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  9. about to only mathematics

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  10. Solve the following sets of equation using Cramer’s rule and remark...

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  11. Solve the following sets of equation using Cramers rule and remark a...

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  12. Determine for that values of lambda and mu the following system of eq...

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  13. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

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  14. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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  15. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

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  16. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

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  17. Using the properties of determinants, find the value of | 0 a -b ...

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  18. Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"...

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  19. If SS(r)=alpha^(r)+beta^(r)+gamma^(r)"then show that "=[{:(,S(0),S(1),...

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  20. If a x1 2+b y1 2+c z1 2=a x1 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d\ a...

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