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Using the properties of determinants, sh...

Using the properties of determinants, show that `abs[[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]]=(1+a^2+b^2)^3`

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Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

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Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

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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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(as...

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  2. Express A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a symmetric and...

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  3. Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b...

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  4. If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...

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  5. Find the minimum value of abs[[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+...

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  6. Find the values of x and y such that [{:(3x+7,5),(y+1, 2-3x):}]=[{:(0,...

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  7. Discuss the continuity of the function defined by f(x)={[x+1, if xle1]...

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  14. Evaluate int(0)^(pi//2)logsinxdx.

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  15. Form the differential equation of the family of all circles of radius ...

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  16. Solve the differential equation frac[dy][dx]=log(x+1)

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  17. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

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  18. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  19. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  20. Prove by vector method that in a parallelogram, the line joining a ve...

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