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Express the matrix [(2,3),(-7,5)] as the...

Express the matrix `[(2,3),(-7,5)]` as the sum of a symmetric and a skew-symmetric and a skew-symmetric matrix.

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

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  2. if A=[(1,2,3),(2,1,-1),(a,2,b)] is a matrix satisfying A A'=9l(3,) fin...

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  3. Express the matrix [(2,3),(-7,5)] as the sum of a symmetric and a skew...

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  4. If A = [(p,q),(r,s)], then express A as the sum of a symmetric and a s...

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  5. show that the matrix A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] is idempotent.

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

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

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

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

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

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

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

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

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  14. Verify that the matrix [(7,-3,-3),(-1,1,0),(-1,0,1)] is the inverse of...

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  15. If A = [(3,1),(-1,2)] then the matrix A^2 - 5A + 8I is

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

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

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

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

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

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