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Prove that any square matrix can be exp...

Prove that any square matrix can be expressed as sum of symmetric and skew symmetric matrix uniquely

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] , then AB an...

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

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  3. Prove that any square matrix can be expressed as sum of symmetric and...

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  4. True or False statements : Every diagonal entry of a skew-symmetric ...

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  5. Match the following

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  6. Let A be a 5 xx 7 matrix, then each column of A contains

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  7. If matrix A is of order 4 xx 3, then each row of matrix A contains ele...

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  8. The numner of all possible matrices of order 2 xx 3 with each entry 0 ...

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  9. The matrix A = [(0,0,6),(0,6,0),(6,0,0)] is a

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  10. The number of all possible matrices of order 3xx3 with each element 0 ...

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  11. If [(2x+y, 4x),(5x-7, 4x)] = [(7,7y-13),(y,x+6)], then the values of x...

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  12. If lambda in R, then lambdaI2 is the matrix

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  13. If A is of order mxxn, B is of order pxxq such that AB is defined, the...

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  14. If P is of order 2xx3 and Q is of order 3 xx 2, then PQ is of order

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  15. If A and B are square matrices of the same order, then (A+B) (A-B) is ...

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  16. If A=[{:(2,-1,3),(-4,5,1):}] and B=[{:(2,3),(4,-2),(1,5):}] , then

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  17. If A is any m xx n matrix, then A^2 can be found only when

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  18. If A=[{:(0,1),(1,0):}] then A^(2) is equal to

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  19. If |x pi| le 1, A = 1/pi [(sin^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi) ,c...

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  20. The matrix [{:(1,0,0),(0,2,0),(0,0,4):}] is a

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