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Using properties of determinants, prove the following `|(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2`.

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Using properties of determinants,prove the following: det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

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Using properties of determinants,prove that det[[-a^(2),ab,acba,-b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
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  2. Find the inverse of A=[[3,-1],[-4,1]] using elementary transformations...

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  3. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  4. If y=(t a n^(-1)\ x)^2 , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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  6. Solve the following differential equation: 2x^2(dy)/(dx)-\ 2x y+y^2=0

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  7. Find the particular solution of the following differential equation...

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  9. Evaluate: int(2x)/((x^2+1)(x^2+3))\ dx

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  10. Evaluate: int(5x+3)/(sqrt(x^2+4x+10))\ dx

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  11. Find the Vector and Cartesian equations of the line passing through...

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  12. Evaluate : int((x-4)e^x)/((x-2)^3)\ dx

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  13. Show that y=log(1+x)-(2x)/(2+x), x gt 1 is an increasing function of x...

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  14. Find the equation of the normal at the point (a m^2, a m^3) for the ...

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  15. Evaluate : int(e^x)/(sqrt(5-4e^x-\ e^(2x)))\ dx

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  16. Find the relationship between a and b so that the function f define...

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  17. If x^y=e^(x-y), show that (dy)/(dx)=(logx)/({log(x e)}^2)

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  18. Obtain the inverse of the following matrix, using elementary operation...

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  19. Using matrices, solve the following system of equations: x+y+z=6; x...

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  20. Find the value of p , if (2 hat i+6 hat j+27 hat k) x ( hat i+3 hat j+...

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