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!

1. 0 belongs to this set because

F*0=0 for any matrix F

2. Let, A and B belong to this set

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

HEnce, A+B is in this set

3. Let, A be in this set and c be a real number

F(cA)=c(FA)=0

Hence, cA is in this set

Hence, H is a subspace