The real eigenvalues for A are 2 and 3 where A 2 0 2 1 3 2

The real eigenvalues for A are 2 and 3, where A = [2 0 -2 1 3 2 0 0 3] Diagonalize A, if possible if not possible explain why.

Solution

Step 1: Transform the matrix to the reduced row echelon form  (Show details)

can be transformed by a sequence of elementary row operations to the matrix

The reduced row echelon form of the augmented matrix is

which corresponds to the system

The leading entries in the matrix have been highlighted in yellow.

A leading entry on the (i,j) position indicates that the j-th unknown will be determined using the i-th equation.

Since every column in the coefficient part of the matrix has a leading entry that means our system has the trivial solution only:

This means the null space consists only of the zero vector, and consequently has no basis.

2 0 -2 1 3 2 0 0 3