3. Linear Algebra

Eigen Theory — Quiz

Test your understanding of eigen theory with 5 practice questions.

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Practice Questions

Question 1

For a linear transformation represented by a matrix $A$, what does an eigenvector represent?

Question 2

What is the determinant of the matrix $\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}$?

Question 3

If a matrix $A$ is diagonalizable, what does this imply about its eigenvectors?

Question 4

Consider a system of differential equations $\mathbf{x}'(t) = A\mathbf{x}(t)$. If $A$ has a positive real eigenvalue, what does this typically indicate about the corresponding solution?

Question 5

Which of the following statements is true about the eigenvalues of a triangular matrix (upper or lower)?