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Express A=[(1,-1),(2,3)] as the sum of a...

Express `A=[(1,-1),(2,3)]` as the sum of a symmetric matrix and a skew symmetric matrix.

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BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  2. Write two non-zero matrices A and B for which AB=0.

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  3. Express A=[(1,-1),(2,3)] as the sum of a symmetric matrix and a skew s...

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  4. Let A=[a(ij)](2times3) where a(ij=i+j. construct A.

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  5. For any square matrix A,prove that A+A' is symmetric.

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  6. If A is a skew symmetric matrix of order 3. Then prove that it's deter...

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  7. Given abs [[2+x,3,4],[1,-1,2],[x,1,5]] is a singular matrix. Find the ...

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  8. Given A and B are square matrices of order 2 such that absA=-1, absB=3...

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  9. For the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)].Find the value of...

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  10. If A=[(3,1),(-1,2)] . Show that A^2-5A+7I=0 Hence find A^4 and A^-1 ...

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  11. Using elementary row operations, find the inverse of the matrix [[1,...

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  12. Find x and y if x[[2],[3]]+y[[-1],[1]]=[[10],[5]]

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

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  14. The value of k such that matrix [[1,k],[-k,1]] is symmetric if

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  15. If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2...

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  16. If A=[[1,3],[4,1]] , then find abs(3A^T)

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  17. If A=[[0,1],[0,0]] ,B=[[1,0],[0,0]], then BA=

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  18. Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric ...

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  19. Find the inverse of A=[[2,-6],[1,-2]]

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  20. Choose the correct statement related to the matrices A=[[1,0],[0,1]]...

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