Orthogonal Diagonalization of a Symmetric Matrix
Consider the symmetric matrix \(A = \begin{pmatrix} 4 & 1 & -2 \\ 1 & 2 & 0 \\ -2 & 0 & 3 \end{pmatrix}\). Answer the following: (a) Confirm that \(A\) is symmetric. (b) Find all eigenvalues and the corresponding eigenvectors of \(A\). (c) Construct an orthonormal basis of \(\mathbb{R}^3\) using the eigenvectors obtained. […]