Question: How find Eigenvectors by considering some points and conditions

By considering matrix A and having three conditions mentioned in maple file, Matrix A  has four zero eigenvalues ​​and one non-zero eigenvalue that are reported in maple file by applying three conditions.

The goal is to obtain five Eigenvectors (V__1` ,`V__2` ,`V__3` ,`V__4` ,`V__5`) corresponding to these five eigenvalues ​​such that they have following form.

1-The first Eigenvector should be v1 = [-, -, -, 0,0] that the three dashes can be whatever, but the last two numbers must be 0 and 0.

2- The second Eigenvector should be v2 = [-, -, -, 0,0] where the three dashes can be anything but the last two numbers must be 0 and 0.

3- The third Eigenvector must be v3 = [-, -, -, 1,0], which three dashes are whatever , but the last two numbers must be 1 and 0.

4-The fourth Eigenvector should be v4 = [-, -, -, 0,1] that those three dashes can be whatever, but the last two numbers must be 0 and 1.
 
5-The fifth  Eigenvector should be v5 = [-, -, -, 0,0] that those three dashes can be whatever, but the last two numbers must be 0 and 0.

for more details please see maple file.

How I can find this Eigenvectors by considering mentioned points.

Thanks

EIGENVECTOR.mw