# Section 7.4 – Basic Theory of Systems of First Order Linear Equations

Directions. The following are review problems for the section. It is recommended you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.
Note: The fundamental matrix mentioned below is discussed in Section 7.7.
1. Given the two vectors $\textbf{x}_1(t)=\begin{pmatrix} 1\\2\\\end{pmatrix}e^t \mbox{ and } \textbf{x}_2(t)=\begin{pmatrix}2\\3\\\end{pmatrix}e^{2t},$ find a differential equation $$\textbf{x'}=\textbf{Ax}$$ for which $$\textbf{x}_1(t)$$ and $$\textbf{x}_2(t)$$ are solutions.

$$\mathbf{x'}=\begin{pmatrix} 5&-2\\6&-2 \end{pmatrix}\textbf{x}$$

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