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Show that abs [[1,a,bc],[1,b,ac],[1,c,ab...

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

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

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

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)

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

Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],[b,c,a],[c,a,b]]

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

MAXIMUM PUBLICATION-MODEL QUESTION-EXAMPLE
  1. Consider the matrix [[1,0,2],[0,1,2],[0,4,9]] Find A^-1 using element...

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  2. Consider the matrix [[1,0,2],[0,1,2],[0,4,9]] Find the solution of th...

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

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  4. If A=[[2,3],[4,-1]] verify that AtimesadjA=absAI

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  5. If f is a function such that f(-x)=f(x), then int(-a)^af(x)dx=………….

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  6. Evaluate int(-pi/2)^(pi/2)cosxdx

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  7. Evaluate int0^1(x^2+1)dx as the limit of a sum.

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  8. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

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  9. Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sq...

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  10. Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sq...

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  11. Show that the lines (x-2)/1=(y+1)/2=(z-3)/1,(x-3)/2=(y-1)/1=(z-4)/2 ar...

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  12. (x-2)/1=(y+1)/2=(z-3)/1,(x-3)/2=(y-1)/1=(z-4)/2 Find the equation of t...

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  13. (x-2)/1=(y+1)/2=(z-3)/1,(x-3)/2=(y-1)/1=(z-4)/2 Show that the above li...

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

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  15. In a circle of radius 2 a square is inscribed as shown in the figure. ...

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  16. If f(x)=sinx,g(x)=x^2,x in R , then find (fog)(x)

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  17. Let u and v be two functions defined on R as u(x)=2x-3 and v(x)=(3+x)/...

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  18. For the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)].Find the value of...

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  19. From the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)], verify AA' and...

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  20. Find the slope of tangent line to the curve y=x^2-2x+1

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