Question

A=

1 1

0 1

Calculate A2, A3, A4,. . . Until you detect a pattern. Write a general formula for An

Answer 1

`A_n=\left[\begin{array}{cc}1&n\\0&1\end{array}\right]`

Explanation:

You want the general formula for the n-th power of matrix A, where ...

`A=\left[\begin{array}{cc}1&1\\0&1\end{array}\right]`

Sequence

The sequence of powers A, A², A³, A⁴ is shown in the attachment. It strongly suggests that the upper right element of the matrix is equal to the power.

The formula for An is ...

`\boxed{A_n=\left[\begin{array}{cc}1&n\\0&1\end{array}\right]}`