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Let A be a square matrix. Then prove tha...

Let A be a square matrix. Then prove that `A A^(T)` and `A^(T) A` are symmetric matrices.

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MODERN PUBLICATION-MATRICES-Exercise 3 (e ) Long Answer Type Questions (I)
  1. If A=[[1,2,3],[-1,0,2],[1,-3,1]], B=[[4,5,6],[-1,0,1],[2,1,2]], C=[[-1...

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  2. If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that Aprime...

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  3. If A=[(sinalpha,cosalpha),(-cosalpha,sinalpha)], the prove that A'A=I.

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  4. A=[(-1,3,0),(-7,2,8)],B=[(-5,0),(0,3),(1,-8)]. then AB

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  5. A=[(3,4),(4,5)],B=[(5,3),(2,1)] then AB is ?.

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  6. If A=[(5,-1),(6,7)],B=[(2,1),(3,4)] and C=[(1,3),(-1,4)], verify the f...

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  7. Let A be a square matrix. Then prove that A A^(T) and A^(T) A are symm...

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  8. Verify that : A+A' is a Symmetric Matrix.

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  9. Verify that : A-A' is Skew - symmetric Matrix when : (i) A=[(1,5),(6...

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  10. for the matrix A=[{:(1,5),(6,7):}], verify that : (I) (A+A') is a sy...

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  11. for the matrix A=[{:(1,5),(6,7):}], verify that : (I) (A+A') is a sy...

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  12. If A=[(3,1,-1),(0,1,2)], then show that A A' is a symmetric matrix.

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  13. If A=[[0,a,b],[-a,0,c],[-b,-c,0]], find 1/2 (A+A\') and 1/2 (A-AA\')

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  14. Express the matrix [{:(2,3,1),(1,-1,2),(4,1,2):}] as the sum of a symm...

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  15. Express [(3,-4),(1,-1)] as the sum of symmetric and skew-symmetric ma...

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  16. Prove that diagonal elements of a skew symmetric matrix are all zeroes...

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  17. Show that the matrix B^TA B is symmetric or skew-symmetric according a...

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  18. Let A and B be symmetric matrices of the same order. Then show that : ...

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  19. Let A and B be symmetric matrices of the same order. Then show that : ...

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  20. If A and B are symmetric matrices of the same order, show that AB+BA i...

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