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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- September 29th 2009, 11:11 AMamm345Matrices- 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. - September 29th 2009, 11:15 AMpomp
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.