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Let A=[3 2 7 1 4 3-2 5 8] . Find matrice...

Let `A=[3 2 7 1 4 3-2 5 8]` . Find matrices `X` and `Y` such that `X+Y=A` , where `X` is a symmetric and `Y` is a skew-symmetric matrix.

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To solve the problem of finding matrices \(X\) and \(Y\) such that \(X + Y = A\), where \(X\) is a symmetric matrix and \(Y\) is a skew-symmetric matrix, we can follow these steps: ### Step 1: Define the Given Matrix \(A\) The matrix \(A\) is given as: \[ A = \begin{bmatrix} 3 & 2 & 7 \\ ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[3-4 1-1] , show that A-A^T is a skew symmetric matrix.

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  2. If the matrix A=[5 2x y z-3 4t-7] is a symmetric matrix, find x ,\ y ,...

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  3. Let A=[3 2 7 1 4 3-2 5 8] . Find matrices X and Y such that X+Y=A , wh...

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  4. Express the matrix A=[4 2-1 3 5 7 1-2 1] as the sum of a symmetric and...

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  5. Define a symmetric matrix. Prove that for A=[2 4 5 6] , A+A^T is a ...

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  6. Express the matrix A=[3-4 1-1] as the sum of a symmetric and a skew-sy...

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  7. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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

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  9. If A=[2 1 4 4 1 5] and B=[3-1 2 2 1 3] . Write the orders of A B and B...

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  10. If A=[4 3 1 2] and B=[-4 3] , write A B .

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  11. If A=[1 2 3] , write AA^T .

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  12. Give an example of two non-zero 2xx2 matrices A and B such that A B...

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  13. If A=[2 3 5 7] , find A+A^T .

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  14. If A=[i0 0i] , write A^2 .

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  15. If A=[(cosx,sinx),(-sinx,cosx)] , find x satisfying 0<x<pi/2 when A+A^...

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  16. If A=[(cosx,-sinx),(sinx,cosx)] , find AA^T

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  17. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

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  18. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  19. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

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  20. If A=[-1 0 0 0-1 0 0 0-1] , find A^2 .

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