(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Orthogonally diagonalize the matrix:

| 2 1 1|

| 1 2 1|

| 1 1 2|

2. Relevant equations

Since this only has three of the same eigenvalues ( lambda = 2), how do i use

A = PD(P^t)? What is P?

After row reduction, I got x = y = z = 1. This would give me the first column of P, but what about the other two columns?

3. The attempt at a solution

This is a symmetric matrix and the eigen values are lambda = 2,2,2

solving (2I - A)x = 0 i get | 0 1 1 |

| 1 0 1 |

| 1 1 0 |

After row reduction: | 1 0 0 |

| 0 1 0 |

| 0 0 1 |

Which means x = y = z = 1?

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# Orthogonal Diagonalization

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