
Matrix Exponential and Eigenvalues

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

Emma Peterson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary goal of the problem introduced in the video?
To find the inverse of a matrix
To determine the rank of a matrix
To solve a system of linear equations
To compute the matrix exponential and find the general solution to X' = A * X
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the eigenvalues of matrix A?
Solving the system of equations
Setting up the determinant equation
Finding the inverse of matrix A
Calculating the trace of matrix A
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which eigenvalue corresponds to the eigenvector (1, 0, 1)?
λ = 1
λ = 2
λ = 3
λ = 4
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the form of matrix D in the matrix exponential calculation?
A diagonal matrix with eigenvalues on the main diagonal
A matrix with zeros on the main diagonal
An identity matrix
A matrix with random values
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of matrix E in the matrix exponential e^(tA)?
It is the inverse of matrix A
It is formed using the eigenvectors as columns
It is a diagonal matrix
It is the identity matrix
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the matrix exponential e^(tA) expressed in terms of matrices E, D, and E inverse?
D * e^(tE) * D inverse
E inverse * e^(tD) * E
E * e^(tD) * E inverse
E * D * E inverse
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the general solution to X' = A * X expressed as?
X = e^(tA) * C
X = A * e^(tC)
X = C * e^(tA)
X = e^(tC) * A
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