IB Mathematics Applications & Interpretation Question Type 2: Finding the Eigenvectors Corresponding to Eigenvalues of a 2x2 Matrix Exercises

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}5& 4\\ 2& 3\end{array}\right)$.

Find the eigenvectors of the matrix $A=\left(\begin{array}{cc}3& 0\\ 0& 2\end{array}\right)$ corresponding to its eigenvalues.

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

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}4& -1\\ 2& 1\end{array}\right)$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}1& 2\\ 2& 1\end{array}\right)$.

Find the eigenvectors of the matrix $A=\left(\begin{array}{cc}5& 0\\ 0& 5\end{array}\right)$ corresponding to its eigenvalues.

Find the eigenvectors of the matrix $A=\left(\begin{array}{cc}2& 1\\ 0& 2\end{array}\right)$ corresponding to its eigenvalues.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}2& 1\\ 1& 2\end{array}\right)$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}0& 1\\ -2& 3\end{array}\right)$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}6& -2\\ 1& 3\end{array}\right)$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}4& 2\\ 1& 3\end{array}\right)$.

Find the eigenvalues and corresponding eigenvectors of the matrix $A=\left(\begin{array}{cc}1& 3\\ 2& 4\end{array}\right)$.