
Understanding Eigenvalues and Eigenvectors in Linear Systems

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary focus of the eigenvalue method discussed in this lesson?
Solving non-linear systems
Finding repeated eigenvalues in matrices
Solving quadratic equations
Calculating determinants
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the algebraic multiplicity of an eigenvalue?
The trace of the matrix
The determinant of the matrix
The number of linearly independent eigenvectors
The number of times an eigenvalue appears in the characteristic equation
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many linearly independent eigenvectors are needed for a complete solution?
One
Two
Equal to the size of the matrix
None
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of this lesson, what does it mean if an eigenvalue is complete?
It is a complex number
Its geometric multiplicity equals its algebraic multiplicity
It is zero
It has no corresponding eigenvectors
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a defective eigenvalue?
An eigenvalue that is zero
An eigenvalue that is complex
An eigenvalue with higher algebraic multiplicity than geometric multiplicity
An eigenvalue with no corresponding eigenvectors
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the defect of an eigenvalue?
The trace of the matrix
The sum of all eigenvalues
The product of all eigenvalues
The difference between algebraic and geometric multiplicities
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens if the geometric multiplicity of an eigenvalue is less than its algebraic multiplicity?
The eigenvalue is doubled
The eigenvalue is ignored
The eigenvalue is considered defective
The eigenvalue is considered complete
Tags
CCSS.HSA.REI.C.9
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