(All Steps) Orthogonally diagonalize the matrix A=[ccc1 2 -2 , 2 3 0 , -2 0 3] What is an eigenbasis corresponding to λ=3 ? Find the orthonormal
Question: Orthogonally diagonalize the matrix \(A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & 3 & 0 \\ -2 & 0 & 3\end{array}\right]\)
- What is an eigenbasis corresponding to \(\lambda=3\) ?
- Find the orthonormal vectors \(\mathbf{v}_{1}, \mathbf{v}_{2}\), and \(\mathbf{v}_{3}\) by applying the Gram-Schmidt procedure to the eigenbasis vectors of \(A\)
- What is the diagonal matrix \(D={{P}^{T}}AP\) ?
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