Question Type 3: Finding the diagonalization matrix of a 2x2 matrix using its eigenvalues and eigenvectors Exercises

Find matrices $P$ and $D$ such that $A = P D P^{-1}$ for $A = \begin{pmatrix}4 & 1\\0 & 2\end{pmatrix}$.

Find the diagonalization of $A=\begin{pmatrix}2 & 3\\3 & 2\end{pmatrix}$ by determining $P$ and $D$.

Find matrices $P$ and $D$ such that $A=PDP^{-1}$ for $A=\begin{pmatrix}4 & 2\\1 & 3\end{pmatrix}$

Diagonalize the matrix $A = \begin{pmatrix} 6 & 1 \\ 0 & 6 \end{pmatrix}$ or explain why it cannot be diagonalized.

Determine whether $A = \begin{pmatrix}1 & 0\\1 & 1\end{pmatrix}$ is diagonalizable. If yes, find $P$ and $D$; if not, explain why.

Find the diagonalization of the matrix $A = \begin{pmatrix}3 & 1\\1 & 3\end{pmatrix}$ by determining an invertible matrix $P$ and a diagonal matrix $D$ such that $P^{-1}AP = D$.

Diagonalize the matrix $A = \begin{pmatrix}2 & 0\\0 & 3\end{pmatrix}$ by finding matrices $P$ and $D$ such that $A = P D P^{-1}$.

Diagonalize the symmetric matrix $A=\begin{pmatrix}2 & 1\\1 & 2\end{pmatrix}$ by finding $P$ and $D$.

Diagonalize the matrix $A=\begin{pmatrix}7 & 2\\2 & 3\end{pmatrix}$ by finding $P$ and $D$.

Diagonalize $A = \begin{pmatrix}1 & 2\\2 & 1\end{pmatrix}$ by finding $P$ and $D$ such that $A=PDP^{-1}$.

Find matrices $P$ and $D$ such that $A=PDP^{-1}$ for $A=\begin{pmatrix}0 & 1\\-2 & 3\end{pmatrix}$.

Diagonalize $A=\begin{pmatrix}5 & 4\\1 & 2\end{pmatrix}$ by computing $P$ and $D$.