
Eigenvalues and Phase Portraits

Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Hard

Thomas White
FREE Resource
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8 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary focus of this video tutorial?
Learning about matrix operations
Understanding calculus concepts
Graphing phase portraits for linear systems
Solving quadratic equations
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a phase portrait, what does the arrow on a solution trajectory represent?
The direction of the X-axis
The time variable
The Y-axis direction
The magnitude of the vector
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which type of eigenvalues result in different graphing methods for phase portraits?
Repeated eigenvalues
Imaginary eigenvalues
Complex eigenvalues
Real eigenvalues
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to solution trajectories when both eigenvalues are positive?
They form a saddle point
They trend towards the origin
They trend away from the origin
They oscillate around the origin
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How are solution trajectories affected when both eigenvalues are negative?
They oscillate around the origin
They form a saddle point
They trend towards the origin
They trend away from the origin
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic of a phase portrait with one positive and one negative eigenvalue?
Center
Saddle point
Unstable node
Stable spiral
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the stability of a system with repeated positive eigenvalues?
Stable
Center
Unstable
Saddle
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In systems with complex eigenvalues, what does the real part determine?
The stability of the system
The frequency of oscillation
The magnitude of oscillation
The direction of oscillation
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