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Consider the following statement P(n):...

Consider the following statement
`P(n):A^n=[[cosntheta,sinntheta],[-sinntheta,cosntheta]]` for all `ninN`
If `P(k)` is true then show that `P(k+1)` is true

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A N EXCEL PUBLICATION-MATRICES-QUESTION BANK
  1. Given A = [(3,2,0),(1,4,0),(0,0,5)] Prove that A^2 -7A +10I3 = 0

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  2. Given A = [(3,2,0),(1,4,0),(0,0,5)] Find A^2

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  3. Consider the following statement P(n):A^n=[[cosntheta,sinntheta],[-s...

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  4. Consider the following statement P(n):A^n=[[cosntheta,sinntheta],[-s...

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  5. Consider the following statement P(n):A^n=[[cosntheta,sinntheta],[-s...

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  6. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  7. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  8. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  9. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  10. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  11. Compute the following: [[a,b],[-b,a]]+[[a,b],[b,a]]

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  12. Compute the following: [[a^2+b^2, b^2+c^2],[a^2+c^2, a^2+b^2]]+[[2ab...

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  13. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  14. Compute the following: [[cos^2x, sin^2x],[sin^2x, cos^2x]]+[[sin^2x,...

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  15. Compute the following: [[a,b],[-b,a]][[a,-b],[b,a]]

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  16. Compute the following: [1 \ 2 \ 3]+ [2 \ 3 \ 4]

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  17. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  18. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  19. Compute the following: [[2,1],[3,2],[-1,1]] [[1,0,1],[-1,2,1]]

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  20. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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