Show wether the vectors are linear independent and if they generate .

a)

My attempt : I don't understandanythingabout my teacher's notes. So I've read on wikipedia that in order to determine if some vectors are l.i. I could calculate the determinant of a matrix formed by them. That's what I did here and I found it to be different from , so the 3 vectors are l.i.

Now how can I show that they generate or not? I guess I must find a basis (but I don't know how to procede and what it is) and check if it generates .

Thanks in advance.