Question Type 2: Finding the eigenvectors corresponding to eigenvalues of a 2x2 matrix Exercises

Find the eigenvectors of the matrix $A = \begin{pmatrix}3 & 0\\0 & 2\end{pmatrix}$ corresponding to its eigenvalues.

Find the eigenvectors of the matrix $A = \begin{pmatrix}5 & 0\\0 & 5\end{pmatrix}$ corresponding to its eigenvalues.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}4 & 2\\1 & 3\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\1 & 2\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}1 & 2\\2 & 1\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}4 & -1\\2 & 1\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}5 & 4\\2 & 3\end{pmatrix}$.

Find the eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\0 & 2\end{pmatrix}$ corresponding to its eigenvalues.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}0 & 1\\-2 & 3\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}6 & -2\\1 & 3\end{pmatrix}$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}1 & 3\\2 & 4\end{pmatrix}$.

Find the eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\-1 & 4\end{pmatrix}$ corresponding to its eigenvalue(s).