Hello,
I need help in this linear Algebra problem...
Prove that W1 = {(a1, a2, a3....a3) E F^n: a1+a2+a3+...+an = 0} is a subspace of F^n, but
W2 = {(a1, a2, a3....a3) E F^n: a1+a2+a3+...+an = 0} is not...
Thanks for the help in advance!
Hello,
I need help in this linear Algebra problem...
Prove that W1 = {(a1, a2, a3....a3) E F^n: a1+a2+a3+...+an = 0} is a subspace of F^n, but
W2 = {(a1, a2, a3....a3) E F^n: a1+a2+a3+...+an = 0} is not...
Thanks for the help in advance!
What is written leads to , perhaps we should replace by in the definition of . If so, since a subspace of a vector space must contain and that we can conclude that doesn't contain and isn't a vector space.
By the way, contains So the only thing we have to prove now is that for every (if is a -vector space),
Let and be two elements of since
Therefore , and is a subspace of