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For any square matrix A with real number...

For any square matrix `A` with real number entries.Prove that `A+A^'` is a symmetric matrix and `A-A^'` is a skew symmetric matrix.

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V PUBLICATION-MATRICES-QUESTION BANK
  1. If A=[[3 ,sqrt3, 2],[ 4 , 2, 0]] and B=[[2 , (-1), 2],[ 1, 2, 4...

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  2. If A=[[-2],[4],[5]] B=[[1,3,6]] (AB)^T=B^TA^T

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  3. For any square matrix A with real number entries.Prove that A+A^' is a...

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  4. Prove that any square matrix can be expressed as the sum of a symmetic...

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  5. Express the matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a ...

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  6. Find the transpose of each of the following matrices: (i) [[5], [1/2]...

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  7. If A=[[-1, 2, 3],[ 5, 7, 9],[ -2, 1 , 1]] and B=[[-4 , 1, -5],[ ...

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  8. If A^'=[[3, 4],[ -1, 2],[ 0, 1]] and B=[[-1, 2 , 1],[ 1,2, 3]] ...

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  9. If A^'=[[-2, 3],[ 1, 2]] and B=[[-1, 0],[ 1, 2]], then find (A+2...

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  10. For the matrices A and B verify that, (AB)^'=B^' A^', where i) A=[[1...

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  11. if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]], then verify A^T...

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  12. show that the matrix A= [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric mat...

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  13. For the matrix A=[[1 , 5],[ 6 , 7]], verify that i) (A+A^') is a sym...

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  14. Find 1/2 (A+A^T) and 1/2(A-A^T) where A=[[0,a,b],[-a,0,c],[-b,-c,0]]

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  15. Express the following matrices as the sum of a Symmetric and a Skew Sy...

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  16. If A, B are symmetric matrices of same order, then AB-BA is a A) skew...

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  17. If A=[[cos alpha, -sin alpha],[sin alpha, cos alpha]], then A+A^T=I if...

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  18. Find P^(-1), if it exists, given P = [(10,-2),(-5,1)]

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  19. Find the inverse of each of the matrices using elementary operations [...

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  20. Find the inverse of the following using elementary transformations. A=...

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