# Cayley-Hamilton

by Yu ·

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### More from my site

- Linear Algebra Midterm 1 at the Ohio State University (1/3) The following problems are Midterm 1 problems of Linear Algebra (Math 2568) at the Ohio State University in Autumn 2017. There were 9 problems that covered Chapter 1 of our textbook (Johnson, Riess, Arnold). The time limit was 55 minutes. This post is Part 1 and contains the […]
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- Find the Formula for the Power of a Matrix Using Linear Recurrence Relation Suppose that $A$ is $2\times 2$ matrix that has eigenvalues $-1$ and $3$. Then for each positive integer $n$ find $a_n$ and $b_n$ such that \[A^{n+1}=a_nA+b_nI,\] where $I$ is the $2\times 2$ identity matrix. Solution. Since $-1, 3$ are eigenvalues of the […]