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If A = {:((cosalpha, sinalpha),(-sinalph...

If `A = {:((cosalpha, sinalpha),(-sinalpha,cosalpha))`, find `'alpha'` satisfying `0 < alpa < pi/2` when `A + A^T = sqrt2I_2`, where `A^T` is transpose of A.

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PRADEEP PUBLICATION-MATRICES-EXERCISE
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  2. If A = [(cos alpha , sin alpha),(-sinalpha, cosalpha)], verify that A ...

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  3. If A = {:((cosalpha, sinalpha),(-sinalpha,cosalpha)), find 'alpha' sat...

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

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  9. Express each of the matrices [(6,3,-2),(5,7,9),(4,7,1)] as the sum of ...

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  10. If A and B are symmetric matrices of the same order. Show that A-B is ...

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  11. If A and B are skew-symmetric matrices of the same order. Show that A-...

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  12. If A is any square matrix, show that 1/2(A + A') is symmetric and 1/2(...

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  13. If A and B are square matrices of the same order and A is symmetric, t...

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  14. If A is a symmetric matrix, prove that A^n is also symmetric for all p...

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  15. Verify that [(2,3),(5,7)] is inverse of the matrix [(-7,3),(5,-2)]

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  16. Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos...

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  19. If Matrix A= [[5,3],[-1,-2]], then show that A^2-3A-7I=0 and hence fin...

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  20. Using the elementary row operations, find the inverse of each of the f...

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