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Prove without expanding that |[bc,a,a^2]...

Prove without expanding that `|[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|`

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Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}| = |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0

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Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

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Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

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SHARAM PUBLICATION-MODEL QUESTION PAPER 13-EXERCISE
  1. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

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  2. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  3. Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^...

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  4. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  5. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  6. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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  7. If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2.

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  8. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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  9. Find the points on the curve x^(2) + y^(2) - 2x - 3 = 0 at which the t...

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  10. For which value of x, the function f(x)=4-x-x^2is maximum or minimum.

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  11. Evaluate int (x+3)^2dx

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  12. Evaluateint0^pi (2/4)sinsqrtxdx

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  13. Evaluate int sin^-1 x dx

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  14. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  15. Solve(dy)/(dt)=e^(3t+5y)

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  16. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  17. If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...

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  18. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  19. Find the equation of the plane passing through (3,-6,-9) and parallel ...

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  20. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

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