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If A = [(1,1),(1,1)], prove by induction...

If `A = [(1,1),(1,1)]`, prove by induction that `A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))]` for all natural numbers n.

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. If A = [(1,1),(1,1)], prove by induction that A^n = [(2^(n-1), 2^(n-1)...

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  2. IF a matrix has 12 elements, what are the possible orders it has 7 ele...

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  3. Give an examples of a matrix which is a row as well as a column matrix...

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  4. Give an example of a matrix which is a scalar matrix which is not a un...

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  5. Give an example of a matrix which is a diagonal matrix which is not a ...

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  6. Classify the following matries: [ 1 + I - 3 sqrt2 i]

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  7. Classify the following matries: [(sqrt2, 0),(sqrt3,2)]

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  8. Classify the following matries: [(2,0,3,5),(0,1,-1,2)]

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  9. Classify the following matries: [(-2,0),(0,1)]

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  10. Classify the following matries: [(0,2,2),(2,0,2),(2,2,0)]

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  11. Classify the following matries: [(4,0,0,0),(0,4,0,0),(0,0,4,0),(0,0,...

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  12. Classify the following matries: [(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,...

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  13. Classify the following matries: [(2-i),(-3),(0),(6)]

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  14. Construct a 2 x 3 matrix A = [a(ij)] for which a(ij) = i + j

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  15. Construct a 2 xx 3 matrix A = [a(ij)](2 xx 3) for which a(ij) = i - j

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  16. Construct a 2 xx 3 matrix A = [a(if)] for which a(ij) = i/j

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  17. Construct a 3 xx 5 matrix B = [b(ij)] such that b(ij) = i + j

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  18. Construct a 3 xx 5 matrix B = [b(ij)] such that b(ij) = i - j

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  19. Construct a 3 xx 5 matrix B = [b(ij)] such that b(ij) = = ij

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  20. Construct a 3 xx 5 matrix B = [b(ij)] such that b(ij) = = i/j

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  21. If [(x-y, z),(2x-y, w)] = [(-1,4),(0,5)], find x , y , z and w.

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