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If A=[[2,5],[1,3]] and AB = [[-13,8],[-8...

If `A=[[2,5],[1,3]]` and `AB = [[-13,8],[-8,5]]` find B.

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If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that (AB)^T=B^TA^T were A^T is the transpose of A.

If A= [[2,-2],[4,2],[-5,1]] B= [[8,0],[4,-2],[3,6]] find the martrix X,such that 2A+3X =5B.

If A = [(-3,-4),(4,5)] and B = [(2,-3),(5,-8)] , verify that (AB)^(-1) = B^(-1)A^(-1) .

If A ={1, 2, 3, 4, 5} and B = {1, 2, 3, 7, 8, 9},find the value of n{(A xxB)cap(BxxA)}

If A={:[(1,2,5),(-1,3,-4)]:} and B={:[(3,-2,1),(0,-1,4),(5,2,-1)]:}, show that, (AB)^(T)=B^(T)A^(T) where A^(T) is the transpose of A.

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If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C such that 3A+5B+2C is a null matrix.

If A=[(8,0),(4,-2),(3,6)] and B=[(2,-2),(4,2),(-5,1)] , then find the matrix X, such that 2A+3X=5B .

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UNITED BOOK HOUSE-SET 1-EXERCISE
  1. Solve: tan^(-1)(cotx)+cot^(-1)(tanx)= pi/4

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  2. Prove that |[y+z,z,y],[z,z+x,x],[y,x,x+y]| =4xyz

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  3. If A=[[2,5],[1,3]] and AB = [[-13,8],[-8,5]] find B.

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  4. Evaluate:lim(x to 0)((a^x-b^x)/x)

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  5. If x= t log t,y = (log t)/t, find (dy)/(dx) when t=1

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  6. Evaluate: int (1-1/x^2)e^(x+1/x)dx

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  7. Solve: (dy)/(dx) = 1-x+y-xy

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  8. Show that the function f(x) = 2/3 x^3-6x^2+20x-5 has neither a maximum...

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  9. The radius of a circular plante increased at the rate of 0.002 cm/s. H...

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  10. Find the acute angle between z-axis and the straight line joining the ...

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  11. Prove that the equation of the plane which passes through the point (2...

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  12. Show that the probability that exactly one of the events A and B occur...

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  13. Show that tan^(-1)(1/sqrt3tanx/2)=1/2 cos^(-1)(1+2cosx)/(2+cosx).

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  14. If A = [[1,x,-2],[2,2,4],[0,0,2]] and A^2+2I3=3A Find x, here I3 is th...

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  15. Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

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  16. Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4a...

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  17. If f(x)= tan^(-1)(x/(1+20x^2)) show that f'(x)=5/(1+25x^2)-4/(1+16x^2)...

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  18. Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(d...

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  19. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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  20. Solve: (6x+9y-7)dx= (2x+3y-6)dy

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