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

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

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

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

Find the diagonalization of $A = \begin{pmatrix}3 & 1\\1 & 3\end{pmatrix}$ by determining P and D.

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

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

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

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

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

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

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