Linear independence proof

1. Jan 22, 2006

cateater2000

Hi I just need some help on understanding some general notation in this quesiton:

Prove if {x_1,x_2,..,x_m} is linearly independent then so is {x_1,x_2,...,x_i-1, x_i+1,...,x_m} for every i in {1,2,...,m}.

I don't really understand what the difference between {x_1,x_2,...,x_i-1, x_i+1,...,x_m} for every i in {1,2,...,m} and {x_1,x_2,..,x_m} is.

Any help clarifying this would be great, and any hints for the question would be must appreciated, thanks.

2. Jan 23, 2006

matt grime

The second set omits the i'th vector.

Eg the large set is {a,b,c,d} and there are 4 other sets: {b,c,d}, {a,c,d}, {a,b,d}, {a,b,c}

3. Jan 23, 2006

TD

If you understand that, you can easily prove this by contradiction.
Suppose one of the smaller sets is linearly dependent, then one of its elements is a lineair combination of the others. What does that tell you about the larger set then?