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Without expanding prove that |[1,a,a^(2)...

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]]

Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0

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 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))

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]|

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

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

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

MODERN PUBLICATION-TEST PAPER 5-PROBLEM
  1. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  2. An animal feed company must produce 200kg of a mixture consisting of i...

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  3. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  4. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  5. Find the inverse of the following matrices using elementary transforma...

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  6. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  7. Express as a sum of a symmetric and a skew symmetric matrix: [[2,-1,3]...

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  8. If y=In(x^2 +y^2),then find dy/dx.

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  9. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  10. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  11. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  12. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  13. Evaluate int0^2abs(x^2+2x-3)dx

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  14. solve:ydx-xdy=xydx

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  15. int(xe^x)/(1+x^2)dx

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  16. int0^pi(xdx)/(1+sinx)

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  17. Solve : (x + 2y^3)dy/dx = y.

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

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  19. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  20. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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