Provide 2 examples of linear transformations from R2 rightar

Provide 2 examples of linear transformations from R^2 rightarrow R^2 for which all vectors in the plane are eigenvectors and explain why this is the case.

Solution

1.

The identity transformation

I(x)=x

So all vectors x in R2 are eigenvectors with eigenvalue 1

2.

The 0 transformation

Z(x)=0=0*x