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Let A = [ (cos theta, sin theta),(- sin...

Let ` A = [ (cos theta, sin theta),(- sin theta, cos theta)]`, then show that ` A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]`

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BETTER CHOICE PUBLICATION-MATRICES-Assignment (Section III) Short answer type questions
  1. Find AB and BA when A = [(2,-1,3),(-3,2,0),(5,1,-1)] , B = [(-3,2,...

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  2. If A = [(cos alpha, sin alpha),(sin alpha, cos alpha)] and B = [(cos b...

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  3. Evaluate [(1,3,5)] [(1,0,3),(2,0,1),(0,1,2)][(1),(4),(6)]

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  4. Let A = [ (cos theta, sin theta),(- sin theta, cos theta)], then show...

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  5. If A = [(2,-1),(3,2)] , B = [(0,4),(-1,7)] , find 3 A^(2) - 2B + I(2...

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  6. A = [ (0,0,1),(0,1,0),(1,0,0)] , verify that A^(2) = I

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  7. If A = [ (1,-1),(-1,1)] and A^(2) = kA then find the value of k

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  8. If A = [(2,-2),(-2,2)] and A^(2) = lambda A then find the value of l...

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  9. Solve the matrix equation [(2x,3)][(1,2),(-3,0)] [(x),(3)] = 0

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  10. If [(3,4),(2,x)][(x),(1)]=[(19),(15)] , find the value of x

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  11. Solve the matrix equation [(x,-5,-1)] [(1,0,2),(0,2,1),(2,0,3)][(x),(...

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  12. Solve for x and y, given that [(x,y),(3y,x)][(1),(2)] = [(3),(5)]

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  13. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  14. If A = [ (2,0,1),(2,1,3),(1,-1,0)] then find A^(2) - 3 A + 2 I

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  15. If A = [ (3,-2),(4,-2)] and I = [(1,0),(0,1)] , then find k so that A...

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  16. If A = [(4,3),(2,5)] , find x and y such that A^(2) - x A + y I = 0

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  17. If A = [(1,2),(2,1)], f(x) = x^(2) - 2 x - 3 , show that f(A) = 0

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  18. If A = [(2,3),(-1,2)] f(x) = x^(2) - 4x + 7 show that f(A) = 0

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  19. If A = [(2,3),(-1,2)] find f (A) where f(x) = x^(3) + 3 x ^(2) - 4 x

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  20. Find the value of a and b for which the following holds : [(a,b),(...

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