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Show that abs[[1,a,a^2],[1,b,b^2],[1,c...

Show that
`abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)`

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using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Using properties of determinants prove the following. abs[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Prove that abs[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] =2abc(a+b+c)^3

MAXIMUM PUBLICATION-MODEL QUESTION-EXAMPLE
  1. Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]

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  2. Form the differential equation of the family of all circles touching t...

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  3. Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

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  4. Evaluate int0^2e^xdx as limit of a sum.

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  5. if x=sin^-1frac(3)(5), then which of the following is true.

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  6. Evaluate tan(sin^-1frac(3)(5)+cot^-1frac(3)(2))

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  7. sin^-1(sinx)=x is defined on

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  8. find the value of sin^-1(sinfrac(13pi)(4)).

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  9. Consider the functions f(x)=sinx and g(x)=x^3 Find fog(x)

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  10. Find the shortest distance between the skew lines vecr=(veci+2vecj+vec...

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  11. The figure shows the graph of a function f(x) and it's derivative f^'(...

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  12. The figure shows the graph of a function f(x) and it's derivative f^'(...

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  13. Find dy/dx, if y=log(cos(e^x))

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  14. If y=sin^-1x , prove that (1-x^2)y2-xy1=0

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  15. Evaluate int0^(pi/2) cos2xdx

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  16. Find the area bonded by the curve y=cos2x,x=0,x=pi/2 and x-axis.

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  17. In a factory which manufactures bolts, machines A,B and C manufacture ...

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  18. A coin is tossed 3 times. Find the probability distribution of the num...

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  19. X is a random variable which denotes the number of heads obtained when...

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  20. Equation of a curve is in the form of a third degree polynomial. It ha...

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