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Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z, z-x-y],[ x-y-z, 2x,2x]|=(x+y+z)^3`

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Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

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Using properties of determinants, prove that : |{:((x+y)^(2),zx,xy),(zx,(z+y)^(2),xy),(zy,xy,(z+x)^(2)):}|=2xyz(x+y+z)^(3) .

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Prove the following using properties of determinants det[[x,y,zx^(2),y^(2),z^(2)y+z,z+x,x+y]]=(x-y)(y-z)(z-x)(x+y+z)]|=

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Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
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  2. Differentiate tan^(-1)((sqrt(1-x^2))/x) with respect to cos^(-1)(2xsqr...

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  3. Using properties of determinants, prove that |[2y,y-z-x,2y],[2z,2z, ...

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  4. Write the vector equation of the plane, passing through the point (...

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  5. Let A={1,2,3,...,9} and R be the relation in A xx A defined by (a , b)...

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  7. Evaluate : int(sin^6x+cos^6x)/(sin^2xdotcos^2x)dx

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  8. Find the particular solution of the differential equation e^xsqrt(1-y^...

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  12. Find the distance between the point (7,2,4) and the plane determined b...

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  13. Find the distance of the point (-1,-5,-10) from the point of inters...

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  14. Find the intervals in which the function f(x)=3x^4-4x^3-12 x^2+5 is (a...

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  15. Assume that each born child is equally likely to be a boy or ...

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  16. Let ** be a binary operation, on the set of all-zero real numbers, giv...

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  17. If 2[3 4 5x]+[1y0 1]=[7 0 10 5], find (x-y)dot

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  18. If "sin"(sin^(-1)\ 1/5+cos^(-1)x)=1, then find the value of xdot

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  19. If |[2x,5],[ 8,x]|=|[6,-2],[ 7, 3]|, write the value of x

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  20. Solve the following matrix equation for x : ,[x1][1 0-2 0]-Odot

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