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prove without expanding, |[(a-b),1,a],[b...

prove without expanding, `|[(a-b),1,a],[b-c,1,b],[c-a,1,c]|=|[a,1,b],[b,1,c],[c,1,a]|`

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Prove without expanding |[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 show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the property of determinants and without expanding {:|( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)|:} =0

Without expanding prove that , |{:(1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a):}|=0

Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|=|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

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

Without expanding prove that, abs((1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a)) = 0

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

UNITED BOOK HOUSE-SET 14-EXERCISE
  1. Let S = N xx Nand ast is a binary operation on S defined by (a,b)^**(c...

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  2. Prove that, 2 sin^(-1)x = sin^(-1) (2x sqrt (1-x^2))

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  3. prove without expanding, |[(a-b),1,a],[b-c,1,b],[c-a,1,c]|=|[a,1,b],[b...

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  4. If two matrices A and B of orders 2 xxm and 3xxn respectively are conf...

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  5. Evaluate:underset(xrarr0)lim log(1 + alphax)/(sin betax)

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  6. If y = logxtanx, find (dy)/(dx).

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  7. overset(pi//2)underset(-pi//2)int |sin x|dx =

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  8. Form the diffential equation of family of parabolas having vertex at t...

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  9. If f(x) = (x-1)e^x + 1, show that f(x) is positive for all positive va...

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  10. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

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  11. Find the equation of the plane which passing through the point hati + ...

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  12. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

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  13. A discrete random variable X has the following distribution: find a.

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  14. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

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  15. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  16. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

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  17. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  18. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

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  19. Solve:(dy)/(dx)=(3x + 4y+1)/(-4x+2y-3)

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  20. Solve:(x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

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