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Representation of matrix as the sum of symmetric and skew symmetric matrix

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Example 6 Express the matrix A as the sum of a symmetric and a skew symmetric matrix,[[2,4,67,3,51,2,4]]

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Express the following matrix as the sum of a symmetric and skew symmetric matrix,and [[3,-2,-43,-2,-5-1,1,2]]

Expess the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A=[{:(3,-1,0),(2," "0,3),(1,-1,2):}].

Express the matrix A=[3-41-1] as the sum of a symmetric and a skew-symmetric matrix.

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-PART-1 (MATRICES)
  1. If A=[{:(6,0),(p,q):}] is a scalar matrix then the value of p and q a...

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  2. If B=[{:(6,3),(-2,k):}] is singular matrix then the value of k is

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  3. If A=[{:(1, 3/5, x),(y, -5, -7),(-4,-7,0):}] is a symmetric matrix the...

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  4. [{:(3,2,1):}] [{: ( 2),(-2),(-1):}]=

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  5. If A=[{:(2,0),(0,2):}] then A^(2) - 3I=……

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  6. If A is a square matrix, then A+A^(T) is

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  7. If A and B are any two square matrices of the same order then (A) (AB)...

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  8. If A=[{:(,1,2),(,2,1):}] then adj A=

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  9. If A is a non singular matrix of order 3 then|adj(A)|=……………

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  10. If A^(2) + 5A + 3I =0, |A| ne 0 then A^(-1)=………………..

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  11. If A is non singular then |A|= 0. True or False.

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  12. Inverse of [{:(2,0),(0,3):}] is [{:(1/2,0),(0,1/3):}] True or False.

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  13. If [{:(3,0),(0,2):}][{:(x),(y):}] = [{:(3),(2):}], then x=1 and y=-1. ...

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  14. Representation of matrix as the sum of symmetric and skew symmetric ma...

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  15. If A=[{:(1,2,-5),(2,-3,4),(-5,4,9):}], then A^(T) =A. True or False

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  16. Matrix [{:(a,b,c),(p,q,r),(2a-p, 2b-q, 2c-r):}] is singular. True or F...

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  17. [{:(2,0,0),(3,-1,0),(-7,3,1):}] is a skew symmetric matrix. True or ...

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  18. If A is an mxxn matrix and B is nxxp matrix does A B exist? If yes, wr...

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  19. After applying elementary transformation R(1) - 3R(2) on matrix [{:(3...

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  20. If A and B are two square matrices such that AB=BA then (A-B)^(2) =A^(...

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