Question 1:
Let . If is a maximal linearly independent subset of , show that each vector is a linear combination of the vectors in .
It is clear if . How about ?
Question 2:
Show that for every .
We know that and . Can I conclude from here?
Question 3:
Let . If each vector is a linear combination of vectors . Show that the maximum number of linearly independent vectors in cannot exceed the maximum number of linearly independent vectors in .
I dont know where to start here.