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(Solved): Diagonalize the following matrix. The real eigenvalues are given to the right of the matri ...
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. \[ \left[\begin{array}{lll} 2 & 4 & 4 \\ 4 & 2 & 4 \\ 4 & 4 & 2 \end{array}\right] ; \lambda=-2,10 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. For \( P=, D=\left[\begin{array}{rrr}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 10\end{array}\right] \) B. For \( P=, D=\left[\begin{array}{rrr}-2 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 10\end{array}\right] \). C. The matrix cannot be diagonalized.
Expert Answer
Solution :- Given matrix is ; [244424442]. And,given eigenvalues of given matrix are ; ?=?2,10.