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If A and B are symmetric matrices, prove...

If `A` and `B` are symmetric matrices, prove that `A B-B A` is a skew symmetric matrix.

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BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric ...

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

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

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  4. IfM=[[7,5],[2,3]],then verify the equation M^2-10M+11I2=0

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  5. Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=...

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  6. Let A=[(2,4),(1,-3)] and B=[(1,-1,5),(0,2,6)] Find AB.

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  7. Let A=[(2,4),(1,-3)] and B=[(1,-1,5),(0,2,6)]Is BA defined? Justify yo...

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  8. If A=[[3,1],[-1,2]] then Find A^2

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  9. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

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  10. If A is a square matrix such that A^2=A, then (I+A)^2-3A is equal to ...

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  11. Find A^2-5A+6I if A=[(2,5,8),(6,0,5),(0,-2,0)]

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  12. Consider the matrices A=[(2,1,3),(2,3,1),(1,1,1)] and B=[(-1,2,3),(-2,...

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  13. Consider the matrix A=[[2,1,3],[2,3,1],[1,1,1]] B=[[-1,2,3],[-2,3,1]...

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  14. Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx...

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  15. Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx...

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  16. Let A=[[3,1],[-1,2]] Show that A^2-5A+7I=0

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  17. If A and B are symmetric matrices, prove that A B-B A is a skew symmet...

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  18. Find a 2xx2 matrix A where a(ij)=i+j

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  19. If [(1,2),(3,4)][(3,1),(2,5)]=[(7,11),(k ,23)], then find the value of...

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  20. Find the inverse of the following matrix using elementary operations A...

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