Question

Let $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] .$ Calculate $A^{2}, A^{3}$ $A^{4}, \ldots$ until you detect a pattern. Write a general formula for $A^{n}$

          Let $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] .$ Calculate $A^{2}, A^{3}$ $A^{4}, \ldots$ until you detect a pattern. Write a general formula for $A^{n}$

Added by Emilio M.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Jason Horton

Step 1

$A^{2}=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]=\left[\begin{array}{ll}2 & 2 \\ 2 & 2\end{array}\right]=2\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]=2A$ $A^{3}=A^{2} \cdot A=2A \cdot Show more…

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Let $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] .$ Calculate $A^{2}, A^{3}$ $A^{4}, \ldots$ until you detect a pattern. Write a general formula for $A^{n}$