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If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1...

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.

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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^(T)A^(T) where A^(T) is the transpose of A.

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

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

If A = ((3,1),(0,2)) show that (A^(T))^(-1) = (A^(-1))^(T) where A^(T) is the transpose of A .

If A={:[(1,-1,0),(-1,2,1),(0,1,1)]and B ={:[(1,1,-1),(0,1,-1),(0,0,1)] show that B^(T)AB is a diagonal matrix, where B^(T) is the transpose of B.

If A={:[(0,1,2),(1,2,3),(3,1,1)]and B={:[(2,1,3),(-1,0,1),(3,-1,4)], show that, AB ne BA .

If A={:[(2,-3,-5),(-1,4,5),(1,-3,-4)]:} and B={:[(-1,3,5),(1,-3,-5),(-1,3,5)]:} show that AB = BA = 0, where 0 is the zero matrix of order 3xx3 .

If A=[(1,-2,3),(-4,2,5)] and B=[(2,3),(4,5),(2,1)] , then find AB, BA. Show that AB ne BA .

If A = ((2,1),(3,4)) and B = ((1,-2),(-1,1)) show that, (AB)^(-1) = B^(-1) A^(-1)

If A={:[(2,0,-5),(-3,4,7)] and B={:[(3,1,-1),(4,5,0)] then prove that (A+B)'=A'+B' (A-B)'=A'-B

UNITED BOOK HOUSE-SET 2-EXERCISE
  1. The direction agnles of a straight line are 120^@,45^@,30^@. Is the s...

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  2. Find K, for which the two planes x+ky+5z+2=0 and 3x-2y+kz-1=0 are perp...

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  3. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  4. Find the probability of guessing correctly at least 5 of the eight ans...

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  5. Solve: tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)= tan^(-1)3x.

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  6. If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that...

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  7. If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such t...

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  8. Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c...

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  9. If x^2+y^2= t-1/t and x^4+y^4 = t^2+1/t^2,show that , x^3y (dy)/(dx) =...

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  10. If 2x= y^(1/5)+y^(-1/5) prove that (x^2-1)y2+xy1 = 25y

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  11. Solve: (2x+4y+3)(dy)/(dx)= 2y+x+1

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  12. Solve: x(1-x^2)dy+(2x^2y-y-5x^3)dx=0.

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  13. If the magnitude of difference of two unit vectors is sqrt3, then show...

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  14. If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b...

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  15. Evaluate : int(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)+g(-x)] dx

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  16. Using the definition of difinite integral as the limit of sum , evalua...

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  17. There are three coins, One is two headed coin, another is a biased coi...

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  18. If X follows a binomial distribution with mean 3 and variance 3/2 find...

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  19. A 5 ft long man walks away from the foot of a 12 1/2 ft high lamp post...

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  20. Mark the area bounded by the curves y^2= 4x and x^2= 4y and find the m...

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