
Diagonalization
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Medium
Dr. 332
Used 3+ times
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The stability of a linear time-invariant (LTI) system depends on:
System matrix rank
Input signal
Eigenvalues of system matrix
System gain
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If all eigenvalues of matrix A have negative real parts, the system is
Unstable
Marginally stable
Asymptotically stable
Critically damped
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A matrix A is diagonalizable if:
It has at least one eigenvalue
B. It has real entries
C. It has n linearly independent eigenvectors
D. It is symmetric
It has real entries
It has n linearly independent eigen vectors
It is symmetric
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In control systems, diagonalization is mainly used to:
Increase speed of computation
Simplify controller hardware
Analyze system dynamics and stability
Increase system gain
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which tool is commonly used to perform matrix diagonalization in simulations?
ORCAD
MATLAB
. AutoCAD
LabVIEW
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the system x˙=Ax, if matrix A is diagonal, then:
The system is nonlinear
States are coupled
Each state evolves independently
Eigenvalues cannot be found
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The characteristic equation of a matrix A is given by:
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