Is There a Quicker Way to Find All Possible Values of h for fh(a+bx+cx2+dx3)?

[says]

(0,1,-1,1) and (0,1,-1,-1)

 

[SammyS]

(0,1,-1,1) and (0,1,-1,-1)

In the spirit of your previous submissions, why not

span{(0, 1, -1, 0), (0, 0, 0, 1)} ?

 

[says]

Yes!
I originally though this could be the span:
span{ (0,0,0,1) , (0,1,-1,0) , (0,1,-1,-1) , (0,1,-1,1) }

But then I put each vector into a matrix and row reduced them and got the (0,1,-1,0) and (0,0,0,1) vector.

 

[says]

There is a second part to this question asking if there are any values of h ∈ R such that fh is not an isomorphism? Not sure if I should ask this in a new post or not. I'm not too sure where to start. I've found this problem extremely difficult.

 

[Mark44]

There is a second part to this question asking if there are any values of h ∈ R such that fh is not an isomorphism? Not sure if I should ask this in a new post or not. I'm not too sure where to start. I've found this problem extremely difficult.

Please start a new thread. This one is now at 95 posts. Let's put this one out of its misery...