# Orthogonal Matrix : Diagonalizability

Dtermine whether or not the following matrix

A= 5 0 2

0 5 0

2 0 5

is diagonalizable. If it is, then determine

P'-1(P inverse)AP.

https://brainmass.com/math/linear-algebra/orthogonal-matrix-diagonalizability-17861

#### Solution Preview

If a matrix is diagonalizable, then the matrix will have n ( or in this case 3) independent eigenvalues:

Set up the equation: det(A-rI) = 0 to get the characteristic equations:

| 5-r 0 2 |

| 0 5-r 0 | = 0

| 2 0 5-r|

(5-r)^3 - 4(5-r) = 0

(5-r)[(5-r)^2 - 4] = 0

Thus ...

#### Solution Summary

Eigenvlaues, determinants and inverses are used to determine the diagonlizability of a given matrix.

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