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If [[1,1],[0,1]] , prove that A^n=[[1,n]...

If `[[1,1],[0,1]]` , prove that `A^n=[[1,n],[0,1]]` for all positive integers `ndot`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...

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  2. If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...

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  3. If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive int...

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  4. If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] ...

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  5. If A=[costhetaisinthetaisinthetacostheta] , then prove by principle...

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  6. If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sin...

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  7. If A=[1 1 1 0 1 1 0 0 1] , then use the principle of mathematical in...

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  8. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

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  9. If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...

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  10. If A is a square matrix, using mathematical induction prove that (A...

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  11. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

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  12. Give examples of matrices A and B such that A B!=B A . (ii) A and B...

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  13. Give examples of matrices A and B such that A B=O but B A!=O . (ii)...

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  14. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

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  15. If A and B are square matrices of the same order, explain, why in g...

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  16. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

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  17. If A and B are square matrices of the same order such that A B=B A ...

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  18. Let A=[[1 ,1, 1],[ 3, 3, 3]] , B=[[3,1], [5, 2],[-2, 4]] and C=[[4,2],...

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  19. Three shopkeepers A ,\ B\ a n d\ C go to a store to buy stationary....

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  20. The cooperative stores of a particular school has 10 dozen physics ...

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