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Express the matrix B=[{:(2,-2,-4),(-1,3,...

Express the matrix `B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}]` as the sum of a symmetric and a skew symmetric matrix.

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The correct Answer is:
`[{:(2,-(3)/(2),-(3)/(2)),(-(3)/(2),3,1),(-(3)/(2),1,3):}]+[{:(0,-(1)/(2),-(5)/(2)),((1)/(2),0,3),((3)/(2),-3,0):}]`
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KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. If A=[{:(1,2,5),(5,1,1),(3,0,4):}] then find A-2A'.

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  2. For the matrices A and B, verify that (AB)'=B'A. (i) A=[{:(1),(3),...

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  3. Express the matrix B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}] as the sum of...

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  4. Show that all the diagonals elements of a skew symmetric matrix are ze...

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  5. Prove that if A is a square matrix then ,(i) (A+A') is a symmetric met...

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  6. Express the matrix A=[{:(2,3,4),(5,6,-2),(1,4,5):}] as the sum of a s...

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  7. If a matrix A is a symmetric matrix then show that A^(n) is also a sy...

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  8. Using elementary transformations find the inverse of each of the follo...

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  9. Find the inverse of [{:(7,4),(1,-2):}]

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  10. Find the inverse of each of the following matrices [{:(-1,2),(-3,5):}...

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  11. Find adjoint of each of the matrices [{:(0,1,2),(1,2,3),(3,1,1):}]

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  12. Find inverse of [{:(1,2,1),(3,2,3),(1,1,2):}]

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  13. If A=[{:(costheta,sintheta),(-sintheta,costheta):}] then prove that ...

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  14. Find the matrix X such that , X[{:(5,-7),(-2,3):}]=[{:(-16,-6),(7,2)...

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  15. Find the matrix X such that , [{:(2,-1),(1,0),(-3,4):}]X=[{:(-1,-8...

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  16. Find x, if [1" "x" "1][{:(1,3,2),(2,5,1),(15,3,2):}][{:(1),(2),(x):}]=...

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  17. Find the real numbers x and y so that (xI+yA)^(2)=A, where A=[{:(0,1),...

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  18. For square matrices A and B , AB=A and BA =B, then prove that A^(2)=A...

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  19. If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then prove...

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  20. If A=[{:(4,x+2),(2x-3,x+1):}] is symmetric matrix then find x.

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