Diagonalize a Matrix

[Kwahha]

Could somebody show me how to diagonalize this matrix?

1 2 2
2 1 2
2 2 3

 

[Deleted member 4993]

Could somebody show me how to diagonalize this matrix?

1 2 2
2 1 2
2 2 3

Do you know how to find eigenvalues of this marix?

 

[Ishuda]

Could somebody show me how to diagonalize this matrix?

1 2 2
2 1 2
2 2 3

What can you use? For example, the Gauss-Jordan elimination method can be used to reduce the row to a diagonal matrix. There are three types of elementary row operations in the method: 1) Swapping two rows, 2) Multiplying a row by a non-zero number, 3) Adding a multiple of one row to another row. So, for example, you could start by subtracting twice the first row from the second row and then subtracting twice the first row from the third row to make the first column (1 0 0)^T. Then continue in that fashion.