Which two of the following subsets of R4are closed under the usual operation of multiplication by scalars? Give Proof as well
1- {(a, b, c, d)| ab=0}
2- {(a, b, c, d)| a=1 b=0 c+d=1}
3- {(a, b, c, d)| a>0 and b<0}
4- {(a, b, c, d)| a>0 and b>0}
5- {(a, b, c, d)| a+b+c+d=0}
1- {(a, b, c, d)| ab=0}
2- {(a, b, c, d)| a=1 b=0 c+d=1}
3- {(a, b, c, d)| a>0 and b<0}
4- {(a, b, c, d)| a>0 and b>0}
5- {(a, b, c, d)| a+b+c+d=0}
-
1 and 5