Fix a 3 times 2 matrix F If H is the set of all matrices A i

Fix a 3 times 2 matrix F. If H is the set of all matrices A in M_2 times 4 so that FA = 0, is H a subspace of M_2 times 4? Justify!

Solution

1. 0 belongs to this set as, F*0=0

2. Let, A,B belong to this set

F(A+B)=FA+FB=0+0=0

3. Let A belong to this set and c be real

F(cA)=cFA=0

Hence ti is a subspace