Homework SourseLet F2 be the field with two elements List all subspace of F
Let F2 be the field with two elements. List all subspace of (F2)^2 . And prove your list is complete.
Let F2 be the field with two elements. List all subspace of (F2)^2 . And prove your list is complete.
Solution
The two elements are necessarily multiplicative identity and additive identity
Hence F2 consists of (0,1)
F2^2 = F2xF2
will be (0,1)x(0,1)
Hence consists of (0,0) (1,0) (1,1) (0,1)
This list is complete as number of elements = 2x2 =4
