# Thread: vector space over finite field

1. ## vector space over finite field

This question was confusing me so any explanations would be greatly appreciated!

The following question deals with F_3, the finite field with three elements (the three elements are 0, 1, 2). (Addition in F_3 is defined modulo 3, which means that 3=0.)

V = (F_3)^5

T = {x ε V | x1 + x2 + x3 + x4 + x5 = 0}

S = Span({(1, 1, 1, 2, 1), (1, 1, 2, 1, 1), (1, 2, 1, 1, 1), (2, 1, 1, 1, 1), (1, 1, 1, 1, 2)} ⊂ V.

Does S = T? If so, prove it. If not, show this by exhibiting an element of S which is not an element of T.

2. Originally Posted by buckaroobill
This question was confusing me so any explanations would be greatly appreciated!

The following question deals with F_3, the finite field with three elements (the three elements are 0, 1, 2). (Addition in F_3 is defined modulo 3, which means that 3=0.)

V = (F_3)^5

T = {x ε V | x1 + x2 + x3 + x4 + x5 = 0}

S = Span({(1, 1, 1, 2, 1), (1, 1, 2, 1, 1), (1, 2, 1, 1, 1), (2, 1, 1, 1, 1), (1, 1, 1, 1, 2)} ⊂ V.

Does S = T? If so, prove it. If not, show this by exhibiting an element of S which is not an element of T.
What about [2 2 2 2 2]?