Consider .We will show this general vector can be obtained by a linear combination of the first 3 elements. To do that we have to obtain the scalars of the combination.

This means . So we have the scalars for the linear combination.

No you cant directly do that. You should prove the first three elements are linearly independent. And then claim this set is adequate using the fact that the dimension of the space is 3.

If a spanning set has 4 vectors, the dimension of the basis it spansneed notbe 4. I can put 100 more vectors in that spanning set. But that set shall still span . Dont forget that whether it span or is decided by the maximum number of linearly independent vectors in the set.

P.S: Also remember that has 3-tuples and has 4-tuples