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IF A=[{:(3,-4),(1,-1):}] then show that...

IF `A=[{:(3,-4),(1,-1):}]` then show that `A^n=[{:(1+2n,-4n),(n,1-2n):}]` , for any integer `n ge1`.

A

`((3n,-4n),(m,-n))`

B

`((2+n,5-n),(n,-n))`

C

`((3^(n),(-4)^(n)),(1^(n),(-1)^(n)))`

D

`((1+2n,-4),(n,1-2n))`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES - EXERCISE - II
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  2. If I = [(1,0),(0,1)] and E = [(0,1),(0,0)] then show that (aI + bE)^(3...

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  3. IF A=[{:(3,-4),(1,-1):}] then show that A^n=[{:(1+2n,-4n),(n,1-2n):}]...

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

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  5. If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)...

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  6. If A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)=

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  7. If A^(2)=2A-I then for n!=2,A^(n)=

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  8. If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

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  9. If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

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  10. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then k =

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  11. IF A=[{:(2,4),(-1,k):}] and A^2=0 then find the value of k

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  12. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

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  13. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

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  14. If [(1,-tan theta),( tan theta,1)][(1,tan theta),(-tan theta, 1)]^-1=[...

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  15. If [[x,4,-1]][(2,1,0),(1,0,2),(0,2,4)][(x),(4),(-1)]=0 then x=

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  16. If A=[a(ij)] is a skew symmetric matrix of order 'n' then suma(ii)=

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  17. The number of 2xx2 matrices that can be formed by using 1,2,3,4 withou...

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  18. If a matrix has 13 elements, then the possible dimensions (orders) of ...

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  19. Statement - I, The matrix [(1,-3,-4),(-1,3,4),(1,-3,-4)] is a nilpote...

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  20. Statement - I If A=[(x,1),(1,0)] is an Involutory matrix then x=0 St...

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