Find the matrix give:

Eigen values are Lamba1 & lambda2 = 1, lambda3 = -2

The eigen spaces are:

E1 = span {[1 1 0],[1 1 1]}, E2 = span {[1 -1 0]}

By normalizing the vectors then computing the matrix A for each composition I obtain:

__|1/2..1/2..0| ___|1/3..1/3..1/3| ___|1/2..-1/2..0|

1*|1/2..1/2..0| +1*|1/3..1/3..1/3| -2*|-1/2..1/2..0|

__|..0....0....0| ___|1/3..1/3..1/3| ___|...0....0....0|

I obtain the matrix:

|-1/6 11/6 1/3|

|11/6 -1/6 1/3|

|1/3 1/3 1/3|

This is the incorrect matrix for the eigenvalues and lambda values given!

I suspect when I formulated the spectral decomposition from the normalized vectors I made and error and thus cascade the incorrect values throughout. Please advise.

Thanks!