Solution: In 21–24, the given vector functions are solutions

Chapter 9, Problem 21E

(choose chapter or problem)

In Problems 21–24, the given vector functions are solutions to the system \(x^{\prime}(t)=A x(t)\) Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution.

\(x_{1}=e^{2 t}\left[\begin{array}{r}  1 \\  -2  \end{array}\right]\)

\(x_{2}=e^{2 t}\left[\begin{array}{r}  -2 \\  4  \end{array}\right]\)

Equation Transcription:

[]

[]

Text Transcription:

x'(t)=Ax(t)

x1=e2t[ -2    1 ]

x2=e2t[   4 -2 ]

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