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If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] t...

If `A=[(1,0),(1,1)]` and `I=[(1,0),(0,1)]` then which one of the following holds for all `nge1`, by the principle of mathematical induction.

A

`A^(n)=nA-(n-1)I`

B

`A^(n)=2^(n-1)A=(n-1)I`

C

`A^(n)=nA+(n-1)I`

D

`A^(n)=2^(n-1)A+(n-1)I`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1A MCQ (ALGEBRA OF MATRICES)
  1. If A^(2)=2A-I then for n>=2,A^(n)=

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  2. fi A=[(1,1),(1,1)] then A^(3)=

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  3. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  4. Find the rank of the matrix A=[(1,4),(0,1)],

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  5. If A=[(1,0,0),(1,0,1),(0,1,0)] Then tra(A)

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  6. If A=[(1,1,0),(0,1,1),(0,0,1)] then A^(2)=

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  7. if n is a positive integer and A=[(a,0,0),(0,b,0),(0,0,c)] then A^(n) ...

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  8. If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that...

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  9. If A=[(cos theta, sin theta),(- sin theta, cos theta)] then lim(nto oo...

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  10. If A=[(-cos theta, sin theta),(sin theta, cos theta)] then IAI=

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  11. If A=[(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha,sin^(2...

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  12. If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alph...

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  13. If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)], then A(a...

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  14. If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

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  15. If A=[(0,c,-b),(-c,0,a),(b,-a,0)] then A^(3)=

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  16. If A=[(1,1,3),(5,2,6),(-2,-1,-3)] then A^(3)=

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  17. If A=[(1,1,-2),(0,1,4),(2,3,1)] then A^(3)-3A^(2)-5A=

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  18. A=[{:(1,2,2),(2,1,2),(2,2,1):}], then A^(3) - 4A^(2) -6A is equal to

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  19. If A=[(4,2),(-1,1)] then (A-21) (A-3I)=

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  20. If A=[(8,-6,2),(-6,7,-4),(2,-4,3)] then A(A-3I)(A-15I)=

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