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Find A^(2)-5A+6I, if A=[{:(2,0,1),(2,1,3...

Find `A^(2)-5A+6I`, if `A=[{:(2,0,1),(2,1,3),(1,-1,0):}]`.

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The correct Answer is:
`[{:(1,-1,-3),(-1,-1,-10),(-5,4,4):}]`
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Show that (i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,1),(3,4):}][{:(5,-1),(6,7):}] (ii) [{:(1,2,3),(0,1,0),(1,1,0):}][{:(-1,1,0),(0,-1,1),(2,3,4):}]ne[{:(-1,1,0),(0,-1,1),(2,3,4):}][{:(1,2,3),(0,1,0),(1,1,0):}]

KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. Solve : [{:(x^(2)),(y^(2)):}]+2[{:(2x),(3y):}]=3[{:(7),(-3):}].

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

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  3. Find A^(2)-5A+6I, if A=[{:(2,0,1),(2,1,3),(1,-1,0):}].

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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