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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1993 • Question 2

Question

Math 6410 • ODE Fall 1993 • Question 2

Let \(\operatorname {trace} A(t)\equiv 0\), \(t\in (-\infty ,\infty )\) and let \(\overline {X}(t)\) be a matrix solution of (2) show that \(\det \overline {X}(t)=\text {constant}\), \(t\in (-\infty ,\infty )\).

Raw LaTeX

Let \(\operatorname{trace} A(t)\equiv0\), \(t\in(-\infty,\infty)\) and let
\(\overline{X}(t)\) be a matrix solution of (2) show that
\(\det\overline{X}(t)=\text{constant}\), \(t\in(-\infty,\infty)\).

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Poincare Maps and Periodic Solutions Variation of Constants Formula