Diagonalization

Diagonalization

University

10 Qs

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Diagonalization

Diagonalization

Assessment

Quiz

Mathematics

University

Practice Problem

Medium

Created by

Dr. 332

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10 questions

Show all answers

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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