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Verify that A=[[a,b],[c,d]] satisfies ...

Verify that `A=[[a,b],[c,d]]`
satisfies the equation `A^2-(a+d)A+(ad-bc) I=0` where `I` is the `2`x`2` unit matrix.

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Find the number of equivalence, relations on X ={1,2,3),

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

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  3. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  4. Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=...

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  5. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  6. Find the inverse of the following matrix [{:(0,0,2),(0,2,0),(2,0,0):}]

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  7. Examine the continuity of the following functions at indicated points....

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  8. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  9. Differentiate. x^(sin x)+(tan x)^x

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  10. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  11. etermine the sub-interval of (-(pi)/(2),(pi)/(2)), in which f(x)=tan x...

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  12. Integrate the following int(x+3)/(5-x^2-4x)

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  13. int0^2[x^2]dx

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  14. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  15. Solve the following differential equations (dy)/(dx)+(y)/(x)=x^(2), ...

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  16. Show that the vector area of the triangle whosse vertices have positio...

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  17. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  18. Find the co-ordinates of the point where the line joining (3,4,-5) and...

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

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

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