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Consider the following statement : P(n...

Consider the following statement :
`P(n):A^n=[[1+2n,-4n],[n,1-2n]]` for all `ninN`
If `P(k)` is true, then show that `P(k+1)` is also true.

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MAXIMUM PUBLICATION-MATRICES-EXAMPLE
  1. IF A=[[2,4,3],[1,0,6],[0,-2,-3]], Evalute A+A^T , is it symmetric ? ...

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  2. Consider the following statement : P(n):A^n=[[1+2n,-4n],[n,1-2n]] fo...

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  3. Consider the following statement : P(n):A^n=[[1+2n,-4n],[n,1-2n]] fo...

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  4. Find the matrices A and B if 2A+3B=[[1,2,-1],[0,2,1],[1,2,4]] and A+...

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  5. Construct a 3xx3 matrix A=[a(ij)] where a(ij)=2(i-j)

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  6. Construct a 3xx3 matrix A=[a(ij)] where a(ij)=2(i-j) Show that the m...

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

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

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  9. A=[[1,2,2],[2,1,2],[2,2,1]] , then Find 4A and A^2

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  10. A=[[1,2,2],[2,1,2],[2,2,1]] , then show that A^2-4A=5I3

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  11. Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Find A^T and B^T

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  12. Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Find AB

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  13. Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Show that (AB)^T=...

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  14. A=[[1,-3,1],[2,0,4],[1,2,-2]] Express A as the sum of a symmetric and ...

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  15. Consider a 2xx2 matrix A=[a(ij)] , where a(ij)=(i+j)^2/2 . Write t...

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  16. Consider a 2xx2 matrix A=[a(ij)] , where a(ij)=(i+j)^2/2 . Show th...

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  17. A=[[6,5],[7,6]] is a matrix What is the order of A .

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  18. A=[[6,5],[7,6]] is a matrix Find A^2 and 12A .

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  19. A=[[6,5],[7,6]] is a matrix f(x)=x^2-12x+1 , find f(A) .

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

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