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Let A=|(3, 2, 7),( 1, 4, 3),(-2, 5, 8)| ...

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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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  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 ,2,x], [y, z,-3], [4,t,-7]] is a symmetric matrix,...

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  3. Let A=|(3, 2, 7),( 1, 4, 3),(-2, 5, 8)| . Find matrices X and Y such t...

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

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

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

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

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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 ...

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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 A A^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=[[i,0], [0,i]] , write A^2 .

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  15. If A=[[cosx,sinx],[-sinx,cosx]] , when A + A^T= I find x satisfying 0 ...

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  16. If A=[[cosx,-sinx],[sinx,cosx]] , find A A^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 ...

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

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