
Eigenvalues and Eigenvectors Concepts

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

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the eigenvalue given for the 2x2 matrix in the video?
λ = 5
λ = -3
λ = 3
λ = -5
Tags
CCSS.8.EE.C.8B
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the equation used to find the eigenvectors of a matrix?
A - λI = 0
A + λI = 0
(A - λI)x = 0
(A + λI)x = 0
Tags
CCSS.HSA.REI.C.9
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of subtracting λ times the identity matrix from the given matrix?
A matrix with all zeros
A matrix with all ones
A matrix with modified diagonal elements
A matrix with unchanged elements
Tags
CCSS.8.EE.C.8B
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving the augmented matrix?
Multiplying rows
Subtracting rows
Row reduction to echelon form
Adding rows
Tags
CCSS.8.EE.C.8B
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if there is no pivot in a column of the augmented matrix?
The column is a free variable
The column is zero
The column is dependent
The column is a leading variable
Tags
CCSS.8.EE.C.8B
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the solution parameterized in terms of a free variable?
By setting x1 = t
By setting x2 = t
By setting x1 = 0
By setting x2 = 0
Tags
CCSS.8.EE.C.8B
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What condition must be met for the parameter t in the eigenvector solution?
t cannot be zero
t must be greater than zero
t must be less than zero
t must be zero
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