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A=[{:(2,3,-1),(1,-2,4):}]andB=[{:(1,4),(...

`A=[{:(2,3,-1),(1,-2,4):}]andB=[{:(1,4),(2,5),(-1,3):}]` then verify that (AB) =B'A.

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If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB)^(-1)=B^(-1)A^(-1)

If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB)^(-1)=B^(-1)A^(-1)

If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}] then verify that : (i) (A')=A (ii) (A*B)'=B'*A' (iii) (kA)'=(k*A')

If A=[{:(2,3),(-4,5):}]andB=[{:(1,-2),(3,4):}]

If A=[{:(-1,2,3),(5,7,9),(-2,1,1):}]andB=[{:(-4,1,-5),(1,2,0),(1,3,1):}] , then verify that (i) (A+B)'=A'+B' (ii) (A-B)'=A'-B'.

If A=[{:(2,3),(1,-4):}],B=[{:(1,-20),(-1,3):}] then verify (AB)^(-1)=B^(-1)A^(-1)

If A=[{:(1,2),(4,1),(5,6):}],B=[{:(1,2),(6,4),(7,3):}] , then verify that : (i) (2A+B)=2A'+B' (ii) (A-B)'=A'-B'

A=[{:(5,-1),(6,7):}],B=[{:(2,1),(3,4):}]andC=[{:(1,3),(-1,4):}] then verify that (i) (A)=A (ii) (A+B)=A+B (iii) (3A)'=3A (iv) (AB)'=B'A'

If A=[{:(3,-4),(1,1),(2,0):}]andB=[{:(2,1,2),(1,2,4):}] ,then verify (B*A)^(2)neB^(2)*A^(2) .

If A'=[{:(-2,3),(1,2):}]andB=[{:(-1,0),(1,2):}] then find (A+2B)'.

KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. Two farmers Ramkishan and Gurpreet singh cultivates only three varieti...

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  2. A=[{:(5,-1),(6,7):}],B=[{:(2,1),(3,4):}]andC=[{:(1,3),(-1,4):}] then ...

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  3. A=[{:(2,3,-1),(1,-2,4):}]andB=[{:(1,4),(2,5),(-1,3):}] then verify tha...

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  4. If A=(1)/(3)[{:(1,2,2),(2,1,-2),(-2,2,-1):}] then show that A A'=A'A=...

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  5. If A=[{:(1,2,5),(5,1,1),(3,0,4):}] then find A-2A'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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