Practice question · Multiple choice
A system of coupled ODEs can be decoupled by changing to the eigenvector basis. Why does that make it solvable?
Hints
- Ask what the matrix looks like in the eigenvector basis.
- A diagonal matrix means each row mentions one variable.
Show the answer
C. Because in that basis each equation involves one variable
Why
Diagonalising decouples. The normal modes of a coupled oscillator are exactly these eigen-directions, combinations that move independently while the raw coordinates do not.
Practise Systems of Differential Equations
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