
Eigenvalues and Eigenvectors Concepts

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

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic polynomial used for in the context of eigenvalues?
To calculate the eigenvalues of a matrix
To determine the eigenvectors of a matrix
To find the determinant of a matrix
To solve linear equations
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following best describes an eigenspace?
A space where all eigenvectors are zero
A set of all eigenvectors corresponding to a particular eigenvalue
A space where eigenvalues are negative
A set of all matrices with the same eigenvalue
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the null space of a matrix used for in finding eigenvectors?
To find the eigenvectors corresponding to an eigenvalue
To determine the rank of the matrix
To solve for the inverse of the matrix
To calculate the determinant of the matrix
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the reduced row echelon form used in the context of eigenvectors?
To determine the rank of the matrix
To find the determinant of the matrix
To simplify the matrix for easier calculation of eigenvectors
To calculate the eigenvalues directly
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the eigenvalue 5, what is the span of the eigenvectors?
The line represented by the vector (1, 0)
The line represented by the vector (0, 1)
The line represented by the vector (1, 1)
The line represented by the vector (1/2, 1)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the eigenvalue -1, what is the span of the eigenvectors?
The line represented by the vector (1, 0)
The line represented by the vector (0, 1)
The line represented by the vector (-1, 1)
The line represented by the vector (1, 1)
Tags
CCSS.HSN.VM.A.1
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to a vector when it is an eigenvector of a matrix with eigenvalue 5?
It is reflected across the origin
It is scaled by a factor of 5
It is rotated by 90 degrees
It remains unchanged
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