Linear Combination and Span

A: -6xx+7 is a possible linear combination of xx2+3xx+2 and xx2+3
B: 2xx2+6 is a possible linear combination of xx2+3xx+2 and xx2+3
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

A: L(S)L(S) is a subspace of VV
B: SS is a subset of L(S)L(S)
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Let RR2 be a vector space over RR and SS is a subset of RR2, then
A: if SS≠{0}, L(S)L(S)= RR2
B: if SS={0}, L(S)L(S)={0}
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

A: (4, 4, 3), (2, 3, 9) and (6, 7, 12) span RR3
B: (4, 3, 7), (1, 1, 1) and (0, 0, 0) span RR3
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Let vv1=(2, 7, 3), vv2=(2, 2, 2) and vv3=(-4, 6, -2)
vv3=2vv1 -4vv2
Then,
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation