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If A=[[1,2,3],[3,-2,1],[4,2,1]]"show tha...

If `A=[[1,2,3],[3,-2,1],[4,2,1]]`"show that"`A^3-23A-40I=0`

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MODERN PUBLICATION-TEST PAPER 5-PROBLEM
  1. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  2. Find the inverse of the following matrices using elementary transforma...

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  3. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  4. Express as a sum of a symmetric and a skew symmetric matrix: [[2,-1,3]...

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  5. If y=In(x^2 +y^2),then find dy/dx.

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  6. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  7. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  8. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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

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  10. Evaluate int0^2abs(x^2+2x-3)dx

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  11. solve:ydx-xdy=xydx

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  12. int(xe^x)/(1+x^2)dx

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  13. int0^pi(xdx)/(1+sinx)

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  14. Solve : (x + 2y^3)dy/dx = y.

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  15. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  16. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  17. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  18. Find the direction cosines of the line which is perpendicular to the l...

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  19. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  20. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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