Hi everyone here is a recent problem that has come up in one of my classes.
The vector space is defined as the field of scalars is Z[sub:21n2oy9i]2[/sub:21n2oy9i] = {0,1}, where + and * are done mod 2.
The set of vectors are { [0,0] , [1,0] , [0,1] , [1,1] }
Normal addition and multiplication by scalars.
Question: Verify that Z[sup:21n2oy9i]2[/sup:21n2oy9i](one 2 is super one is sub) is indeed a vector space.
We were told we could either list all possibly cases or use vectors such as [a, b], [c, d] etc. and do it a general way.
I know for the question I have to go through the 10 axioms/rules for vector spaces to show that each one holds up to prove that it is a vector space. I have done it before with much easier cases but this one is giving me lots of trouble. I want to do it the general way but I am not sure how.
Hopefully all of the notation makes sense. Any tips would really be appreciated.
The vector space is defined as the field of scalars is Z[sub:21n2oy9i]2[/sub:21n2oy9i] = {0,1}, where + and * are done mod 2.
The set of vectors are { [0,0] , [1,0] , [0,1] , [1,1] }
Normal addition and multiplication by scalars.
Question: Verify that Z[sup:21n2oy9i]2[/sup:21n2oy9i](one 2 is super one is sub) is indeed a vector space.
We were told we could either list all possibly cases or use vectors such as [a, b], [c, d] etc. and do it a general way.
I know for the question I have to go through the 10 axioms/rules for vector spaces to show that each one holds up to prove that it is a vector space. I have done it before with much easier cases but this one is giving me lots of trouble. I want to do it the general way but I am not sure how.
Hopefully all of the notation makes sense. Any tips would really be appreciated.
