IB Mathematics Applications & Interpretation Question Type 3: Finding the Diagonalization Matrix of a 2x2 Matrix Using Its Eigenvalues and Eigenvectors Exercises

Find matrices $P$ and $D$ such that $A=PD{P}^{-1}$ for $A=\left(\begin{array}{cc}4& 1\\ 0& 2\end{array}\right)$.

Find the diagonalization of $$A=\left(\begin{array}{cc}2& 3\\ 3& 2\end{array}\right)$$ by determining $P$ and $D$.

Find matrices $P$ and $D$ such that $A=PD{P}^{-1}$ for $$A=\left(\begin{array}{cc}4& 2\\ 1& 3\end{array}\right)$$

Diagonalize the matrix $A=\left(\begin{array}{cc}6& 1\\ 0& 6\end{array}\right)$ or explain why it cannot be diagonalized.

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

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

Diagonalize the matrix $$A=\left(\begin{array}{cc}2& 0\\ 0& 3\end{array}\right)$$ by finding matrices $P$ and $D$ such that $$A=PD{P}^{-1}$$.

Diagonalize the symmetric matrix $$A=\left(\begin{array}{cc}2& 1\\ 1& 2\end{array}\right)$$ by finding $P$ and $D$.

Diagonalize the matrix $$A=\left(\begin{array}{cc}7& 2\\ 2& 3\end{array}\right)$$ by finding $P$ and $D$.

Diagonalize $$A=\left(\begin{array}{cc}1& 2\\ 2& 1\end{array}\right)$$ by finding $P$ and $D$ such that $A=PD{P}^{-1}$.

Find matrices $P$ and $D$ such that $A=PD{P}^{-1}$ for $A=\left(\begin{array}{cc}0& 1\\ -2& 3\end{array}\right)$.

Diagonalize $$A=\left(\begin{array}{cc}5& 4\\ 1& 2\end{array}\right)$$ by computing $P$ and $D$.