PLLEEAASEE HELP ME! This is elementary linear algebra.

[smurff4]

Hi, I'm really having a lot of problems with these from my text book, and I am preparing for my exams and am in great need of someone's help please?!?! Please give me step by step solutions to these problems, I need to know how to do them.
1. Show that the vectors v1=(1,2,3,4), v2=(0,1,0,-1), and v3=(1,3,3,3), form a linear dependent set in R^4.

2. Show that if S={v1,v2,...,v sub r} is a linearly independent set of vectors, then so is every nonempty subset of S.

 

[stapel]

1. Show that the vectors v1=(1,2,3,4), v2=(0,1,0,-1), and v3=(1,3,3,3), form a linear dependent set in R^4.

Follow the usual procedure: multiply the vectors by constants (you could call them "a", "b", and "c"), add, set equal to zero, and solve. If you can show that you can get the zero vector without having to have all zero constants, then one of the vectors must be some combination of the others.

2. Show that if S={v1,v2,...,v sub r} is a linearly independent set of vectors, then so is every nonempty subset of S.

I would try a proof by contradiction.

Eliz.