Answer:
H is the span of the vectors (1,-1,1,0), (-3,1,0,1).
Step-by-step explanation:
To begin with remember the following theorem.
Theorem : Given a vector space V let [tex]\{v_1 , ...,v_n\}[/tex] be a set of vectors of the , then [tex]span(\{v_1 , ...,v_n\})[/tex] is a subspace of V.
Notice that any vector, in the described subspace looks like this.
(a-3b , b-a , a , b ) = (a , -a , a , 0 ) + ( -3b , b , 0 , b )
= a( 1 , -1 , 1 , 0 ) + b( -3 , 1 , 0 , 1 )
Therefore H is the span of the vectors (1,-1,1,0), (-3,1,0,1) and according to the theorem it would be a subspace.
