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Using properties of determinants, show the following: `|[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3`

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Using properties of determinants, prove the following |(3a,-a+b,-a+c),(a-b,3b,c-a),(a-c,b-c,3c)|=3(a+b+c)(ab+bc+ca)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
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  3. Using properties of determinants, show the following: |[(b+c)^2,ab, ...

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  8. Find the area of the region included between the parabola y^2=x and...

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  9. Evaluate: int0^pi(x dx)/(a^2cos^2\ \ x+b^2sin^2\ \ x)

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  13. Find the equation of the plane determined by the points (A(3,-1,\ 2...

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  14. Evaluate: int0^pi(xtanx)/(secx+tanx)\ dxdot

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  15. Find the equation of line through the intersection of lines 3x+4y=7 an...

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  16. Differentiate the following with respect to x : x^(sinx)+(sinx)^(cosx)

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  17. Write the differential equation formed from the equation y=m x+c , ...

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  18. If vec a is a unit vector and ( vec x- vec a)dot( vec x+ vec a)=24 , ...

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  19. If A is a square matrix and |A| =2, then write the value of |A A ...

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  20. If A=|[3, 10],[ 2, 7]|, then write A^(-1)

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