
Eigenvalues and Linear Independence Concepts

Interactive Video
•
Mathematics
•
11th Grade - University
•
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 initial task given in the problem statement?
Calculate the determinant of the matrix.
Determine the eigenvalues and defects.
Solve a system of linear equations.
Find the inverse of the matrix.
Tags
CCSS.HSA.REI.C.9
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do we find the eigenvalues of a matrix?
By solving the matrix equation Ax = 0.
By finding the inverse of the matrix.
By calculating the trace of the matrix.
By setting the determinant of (A - λI) to zero.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What indicates that an eigenvalue has an algebraic multiplicity of two?
The eigenvalue is complex.
The eigenvalue is zero.
The eigenvalue has two linearly independent eigenvectors.
The eigenvalue appears twice in the characteristic equation.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a defect in the context of eigenvalues?
When the algebraic multiplicity is less than the geometric multiplicity.
When the algebraic multiplicity is more than the geometric multiplicity.
When the eigenvalue is zero.
When the eigenvalue is complex.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the geometric multiplicity of an eigenvalue?
The product of all eigenvalues.
The number of times the eigenvalue appears in the characteristic equation.
The sum of all eigenvalues.
The number of linearly independent eigenvectors associated with the eigenvalue.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is a second linearly independent solution needed for λ = 1?
To solve a system of linear equations.
To find the inverse of the matrix.
To calculate the determinant of the matrix.
Because the eigenvalue has an algebraic multiplicity of two.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What method is used to find the second linearly independent solution?
Finding the inverse of the matrix.
Solving the equation (A - λI)v = v1.
Solving the equation (A - λI)v = 0.
Calculating the trace of the matrix.
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