I am trying to find the pseudo inverse and SVD as well as single values for a matrix:

Thus far I have been able to (this is condensed a little) the following:

Matrix A is:

|1 1 -1|

|1 1 -1|

SVD:

Matrix *ATA *=

| 2 2 -2|

| 2 2 -2|

|-2 -2 2 |

This matrix has rank 2 so it must have a 2-D nullspace and hence 0 is a double eignevalue. That is the eigenvalues I found to be as:

Lamba2,3 =0, Lambda1 =6.

Thus the corresponding orthonormal eigenvectors are:

V1=1/sqrt(3)*(|1|

|1|

|1|)

V2=1/sqrt(2)*(|1 |

|-1|

| 0|)

V3=1/sqrt(6)*(|1|

|1|

|1|)

Now:

Let V=|V1*V2*V3|

The last two found via satisfying x+y-2z=0 and applying Gram Schmidt to get the orthogonal basis.

Sum=(|alpha1 0 0|

| 0 0 0|)*U1=

Av1/sqrt(6)

= 1/sqrt(2)*(|1|

|1|)

Let U2=1/sqrt(2)*(| 1|

|-11|) to be a vector orthogogonal to u1, and set

u1 = to |u1 u2|

I am trying to finish this problem and it asks to find the Single values, SVD, and Pseudo inverse.