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If A = [(cos alpha , sin alpha),(-sinalp...

If `A = [(cos alpha , sin alpha),(-sinalpha, cosalpha)]`, verify that AA' = I_2 = A'A

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. For the matrices A and B, verify that (AB)' = B'A', where : A = [[1],[...

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  2. For the matrices A and B, verify that (AB)' = B'A', where : A = [[0],[...

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  3. If A = [(cos alpha , sin alpha),(-sinalpha, cosalpha)], verify that AA...

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  4. If A = {:[(sinalpha, cosalpha),(-cosalpha,sinalpha)], then prove that ...

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  5. Show that the matrix A = [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric m...

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  6. Show that the matrix A = [[0,1,-1],[-1,0,1],[1,-1,0]] is a skew symmet...

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  7. For the matrix A=[(1,5),(6,7)], verify that (A+A') is a symmetric matr...

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  8. For the matrix A=[(1,5),(6,7)], verify that (A-A') is a skew symmetr...

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  9. Find (1)/(2)(A+A')and(1)/(2)(A-A'), when A=[(0,a,b),(-a,0,c),(-b,-c,0)...

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  10. Express the following matrices as the sum of a symmetric and a skew sy...

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  11. Express the following matrices as sum of a symmetric and a skew symme...

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  12. Express the following matrices as the sum of a symmetric and skew-symm...

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  13. Express the following matrices as sum of a symmetric and a skew symme...

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  14. If A, B are symmetric matrices of same order, then AB - BA is a :

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  15. If A = [(cosalpha, -sinalpha),(sinalpha, cosalpha)], then A + A' = I, ...

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  16. Using elementary transformation, find the inverse of the following mat...

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  17. Using elemenatry transformations, find the inverse of the following ma...

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  18. Using elemenatry transformations, find the inverse of the following ma...

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  19. Using elemenatry transformations, find the inverse of the following ma...

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

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