Linear Algebra & DEs Quiz

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Quiz on eigenvalues, systems, DE basics.

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Yaj Kotak

United States

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Linear Algebra & DEs Quiz


Froggy Jumps Linear Algebra & DEs QuizOnline version Quiz on eigenvalues, systems, DE basics. by Yaj Kotak 1 1. Which condition guarantees that a set of vectors is linearly independent? a The vectors span the space b One vector is a scalar multiple of another c The only solution to the linear combination equals zero is the trivial solution 2 2. A square matrix A has an eigenvalue lambda if there exists a nonzero vector v such that: a det(A) = 0 b Av = lambda v c Av = 0 3 3. What is the first step in finding the eigenvalues of a matrix? a Row-reduce the matrix b Find the inverse of the matrix c Compute det(A - lambda I) 4 4. If a matrix has complex eigenvalues, what does this indicate about the system? a The solutions involve oscillatory behavior b The system grows exponentially c The system has no solutions 5 5. A repeated eigenvalue occurs when: a The same eigenvalue appears more than once as a root of the characteristic equation b An eigenvalue has magnitude greater than 1 c Eigenvectors are orthogonal 6 6. A homogeneous linear system with constant coefficients has which general property? a It always has the trivial solution b It cannot be solved analytically c It always has exactly one solution 7 7. Directional fields are primarily used to: a Visualize solution behavior of differential equations b Find exact solutions to systems c Test linear independence 8 8. Which differential equation method involves separating variables on opposite sides of the equation? a Euler’s method b Separation of variables c Integrating factor 9 9. Euler’s method is best described as: a An exact solution technique b A matrix-based method c A numerical approximation method 10 10. Reduction of order is used when: a One solution to a second-order differential equation is already known b The equation is separable c A differential equation has constant coefficients

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Linear Algebra & DEs Quiz

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Linear Algebra & DEs QuizOnline version

by Yaj Kotak

1. Which condition guarantees that a set of vectors is linearly independent?

2. A square matrix A has an eigenvalue lambda if there exists a nonzero vector v such that:

3. What is the first step in finding the eigenvalues of a matrix?

4. If a matrix has complex eigenvalues, what does this indicate about the system?

5. A repeated eigenvalue occurs when:

6. A homogeneous linear system with constant coefficients has which general property?

7. Directional fields are primarily used to:

8. Which differential equation method involves separating variables on opposite sides of the equation?

9. Euler’s method is best described as:

10. Reduction of order is used when: