If `A=[(1, 1, 1),( 0, 1, 1), (0, 0, 1)]` , then use the principle of mathematical induction to show that `A^n=[(1,n,{n(n+1)}/2), (0, 1,n),(0, 0, 1)]` for every positive integer `n` .

Explanation

Given that,

`A= [(1, 1, 1),( 0, 1, 1), (0, 0, 1)]`

We have to prove that `A^n=[(1,n,{n(n+1)}/2), (0, 1,n),(0, 0, 1)]` for all positive integers `ndot`

It is true for `n=1`.

`implies A^2= [(1, 1, 1),( 0, 1, 1), (0, 0, 1)]xx [(1, 1, 1),( 0, 1, 1), (0, 0, 1)]`

`implies A^2= [(1,2,3),(0,1,2), (0,0,1)]`

It is true for `n=2`.

Let it is true for `n=n-1`

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