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Math Help - Matrices- Find Formula and Prove by Induction

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    Matrices- Find Formula and Prove by Induction

    Let A be a matrix =
    [1 1 1
    0 1 1
    0 0 1]

    Find a formula for A^n(n is an element of N) and prove the formula by induction.
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  2. #2
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    Quote Originally Posted by amm345 View Post
    Let A be a matrix =
    [1 1 1
    0 1 1
    0 0 1]

    Find a formula for A^n(n is an element of N) and prove the formula by induction.
    Show some working and we can help better. Here is a general way that I would recommend approaching this problem.

    1) Calculate a few powers of A and try to spot a pattern.
    2) Use your findings to speculate what the nth power would be.
    3) Show that your formula works when n = 1.
    4) Show that if your formula holds for n=k, then it also holds for n=k+1.
    5) Smile, because your speculation was correct and you have just proved it by induction.

    Let us know which step you get stuck on.
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