12. Diagonalization and Dynamical Systems

Modeling Iterative Systems — Quiz

Test your understanding of modeling iterative systems with 5 practice questions.

Practice Questions

Question 1

In a discrete linear iterative system, which formula gives the next state from the current state?

Question 2

If $x_{k+1}=Ax_k$ and the initial state is $x_0$, what is $x_3$?

Question 3

A vector $v$ is a fixed point of $x_{k+1}=Ax_k$ when which equation is true?

Question 4

If a matrix is diagonalizable as $A=PDP^{-1}$, what is the formula for $A^n$?

Question 5

If $v$ is an eigenvector of $A$ with eigenvalue $\lambda$, and $x_0=v$, what is $x_k$ for $x_{k+1}=Ax_k$?