Solved: In 29–30, verify that X(t) is a fundamental matrix
Chapter 9, Problem 30E(choose chapter or problem)
In Problems 29–30, verify that \(X(t)\) is a fundamental matrix for the given system and compute \(X^{-1}(t)\). Use the result of Problem 28 to find the solution to the given initial value problem.
\(x^{\prime}=\left[\begin{array}{ll} 2 & 3 \\ 3 & 2 \end{array}\right] x\)
\(x(0)=\left[\begin{array}{r} 3 \\ -1 \end{array}\right]\)
\(x(t)=\left[\begin{array}{cc} e^{-t} & e^{5 t} \\ -e^{-t} & e^{5 t}\)
Equation Transcription:
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Text Transcription:
X(t)
X-1(t)
x'=[ 3 2 2 3 ] x
x(0)=[ -1 3 ]
x(t)=[ -e-t e5t e-t e5t ]
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