
Eigenspaces and Eigenvalues Concepts

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Aiden Montgomery
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a necessary condition for a matrix to have non-trivial eigenvalues?
The matrix must have a determinant of zero.
The matrix must be invertible.
The matrix must be symmetric.
The matrix must be diagonal.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between an eigenvalue and its corresponding eigenvector?
The eigenvalue is the inverse of the eigenvector.
The eigenvector is scaled by the eigenvalue.
The eigenvalue is the square of the eigenvector.
The eigenvector is always zero.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the eigenspace for a given eigenvalue determined?
By calculating the trace of the matrix.
By finding the inverse of the matrix.
By solving the characteristic polynomial.
By finding the null space of the matrix.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the reduced row echelon form used for in the context of eigenspaces?
To determine the rank of the matrix.
To simplify the calculation of the null space.
To find the determinant of the matrix.
To calculate the trace of the matrix.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the eigenspace for lambda = 3 in terms of vectors?
The span of vectors (1, 0, 0) and (0, 1, 0).
The span of vectors (1, 1, 1) and (0, 0, 0).
The span of vectors (1/2, 1, 0) and (1/2, 0, 1).
The span of vectors (0, 0, 1) and (1, 1, 1).
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the eigenspace for lambda = -3 in terms of vectors?
The span of vector (1, 0, 0).
The span of vector (0, 1, 0).
The span of vector (1, 1, 1).
The span of vector (-2, 1, 1).
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the geometric interpretation of the eigenspace for lambda = 3?
A plane in R3.
A hyperplane in R3.
A point in R3.
A line in R3.
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