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If A=[{:(1,alpha),(0,1):}] then by the ...

If `A=[{:(1,alpha),(0,1):}]` then by the principle of mathematical induction . Prove that `A^(n)=[{:(1,nalpha),(0,1):}],AAn inN`.

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KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. If A=[{:(1,0),(-1,7):}]andA^(2)=8A+KI then find K.

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  2. Prove that , {[{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,...

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  3. If A=[{:(1,alpha),(0,1):}] then by the principle of mathematical indu...

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  4. If A=[{:(0,1,2),(2,-3,0),(1,-1,0):}]andf(x)=x^(3)+4x^(2)-x, then find ...

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

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  6. Three friends Ram , Shyam and Rahul went to a shop .Ram purchased 12 d...

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  7. Two farmers Ramkishan and Gurpreet singh cultivates only three varieti...

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

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

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

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

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

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

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

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

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

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

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

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

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

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