Linear Algebra Quiz _ Week 5 - Diagonalization-Dyn. Systems

Linear Algebra Quiz _ Week 5 - Diagonalization-Dyn. Systems

University

13 Qs

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Linear Algebra Quiz _ Week 5 - Diagonalization-Dyn. Systems

Linear Algebra Quiz _ Week 5 - Diagonalization-Dyn. Systems

Assessment

Quiz

Mathematics

University

Easy

Created by

Bobby Bobby

Used 1+ times

FREE Resource

13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following is a necessary condition for a matrix to be diagonalizable?

The matrix must be square.

The matrix must have real eigenvalues.

The matrix must have distinct eigenvalues.

The matrix must have orthogonal columns.

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the relationship between the eigenvectors of a matrix and its diagonalization?

The eigenvectors form a diagonal matrix.

The eigenvectors are the columns of the matrix used to diagonalize.

The eigenvectors determine the eigenvalues.

The eigenvectors are not involved in diagonalization.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a matrix is not diagonalizable, what could be the possible cause?

The matrix has complex eigenvalues.

The matrix does not have enough linearly independent eigenvectors.

The matrix has repeated eigenvalues.

The matrix is symmetric.

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When all eigenvectors are linearly independent.

When the matrix is square.

When the eigenvalue is positive.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The state of the system at any given time.

The transition rule between states.

The initial condition of the system.

The solution of the system.

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