12. Diagonalization and Dynamical Systems

Powers Of Matrices Using Diagonalization — Quiz

Test your understanding of powers of matrices using diagonalization with 5 practice questions.

Practice Questions

Question 1

If $A=PDP^{-1}$, what is the correct formula for $A^5$?

Question 2

Why is diagonalization useful for computing powers of a matrix?

Question 3

If $D=\begin{pmatrix}2&0\\0&-3\end{pmatrix}$, what is $D^4$?

Question 4

If $A=PDP^{-1}$ and $D=\mathrm{diag}(1,4)$, what are the eigenvalues of $A^3$?

Question 5

What condition must a matrix satisfy to use diagonalization to compute its powers in the form $A^n=PD^nP^{-1}$?