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Consider the following. \[ A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 8 & 8 & 1 \\ 9 & 0 & 1 \end{array}\right] \] List the eigenvalues of \( A \) and bases of the corresponding eigenspaces. (Repeated eigenvalue: smallest \( \lambda \)-value \[ \begin{array}{l} \lambda_{1}=\quad \text { has eigenspace span }\left(\mid \begin{array}{ll} \mid \end{array}\right) \Rightarrow \\ \lambda_{2}= \\ \text { * has eigenspace span } \\ \left(\left[\begin{array}{l} \\ \| \\ \Downarrow \mathbb{1} \end{array}\right] \Rightarrow\right. \\ \text { w } \\ \end{array} \]
Determine whether \( A \) is diagonalizable. \[ A=\left[\begin{array}{ll} -5 & 9 \\ -1 & 1 \end{array}\right] \] Yes No Find an invertible matrix \( P \) and a diagonal matrix \( D \) such that \( P^{-1} A P=D \). (Enter each matrix in the form [[row 1\( ],[ \) row 2\( \left.], \ldots\right] \), where each row is a comma-separated list. If \( A \) is not diagonalizable, enter NO SOLUTION.) \[ (D, P)=(\quad) \] [6/8 Points] POOLELINALG4 4.4.012.EP. Consider the following. \[ A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 8 & 8 & 1 \\ 0 & 0 & 1 \end{array}\right] \] Type here to search

8. Given matrix is A=[?59?11]. The characteristic polynomial of the matrix A is |A??I|=0 ?|?5??9?11??|=0 ?(?5??)(1??)?9(?1)=0 ??2+4?+4=0 Solving for ?