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Prove that the following. [[b+c,a,a],[b,...

Prove that the following. `[[b+c,a,a],[b,c+a,b],[c,c,a+b]]`=4ab

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Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2

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MODERN PUBLICATION-TEST PAPER 6-EXERCISE
  1. A merchant sells two models X and Y of TV with cost price ₹ 25000 and ...

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  2. A binary operation * is defined on the set X=R-{-1} by x**y=x+y +xy,...

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  3. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  4. Using determinants, find the values of a if the area of triangle with ...

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  5. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  6. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

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  7. Differentiate tan^-1((2x)/(1-x^2)).

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  8. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

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  9. Find dy/dx if y=(cosx)^x.

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

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  11. Find the interval where y=sin2x-cos2x,xin[0,2pi] is (a) incresing (b)...

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  12. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

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  13. Integrate : int sin^(-1)xdx.

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  14. Find the particular solution of d^2 y/dx^2 =2x,given that x=0,y=2 and ...

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  15. Solve :-(x^2+y^2)dx-2xy dy=0

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  16. If with reference to the eight handed system of mutually perpendicular...

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  17. If vec a =(2,3,6), vec b=(2,-2,1), vec c=(-1,0,2), find the direction ...

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  18. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

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  19. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

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  20. Find the distance of the point (-1,-5,-10) from the point of intersect...

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