Practice Similarity And Systems Of Linear Differential Equations (31.13)

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6 sample questions

Question 1.
What is the form of a linear system of ODEs?
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Recall the basic structure of ODEs.
Question 2.
Define a diagonalizable matrix.
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Think about the eigenvalue representation.
3Question 3.
What form does a linear system of ODEs take?
- dx/dt = Bx
- dx/dt = Ax
- dx/dt = Cx
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Think about the standard representation in ODEs.
4Question 4.
Is a matrix that cannot be diagonalized still useful?
- True
- False
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Consider how we might express systems even without diagonalization.
Question 5.
Given a matrix A = [[3, 1], [0, 3]], determine its eigenvalues and discuss whether the system of ODEs it describes can be simplified using diagonalization.
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Review the characteristic polynomial for solutions.
Question 6.
Consider a linear system represented by dx/dt = A for A = [[0, 1], [-1, 0]]. Describe how this might represent a physical system and analyze its behavior over time by finding its eigenvalues.
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Use the determinant method to find eigenvalues.

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