I shoud show whether and for all and is a linear functional . is a linear transformation. I think no, because the image of the zero vector is not 0. To be honest I am not really sure about these lienar functional thing.

Second. v1 v2 v3 is a basis of V.

. About this I know it is a linear transformation. Is it invertible. I know it would be enough to show its injectivity but how can I do this in this case?

Thank you!