Linear Combinations

Question 1

Linear Combination

Answer 1

k1u1 + k2u2 + …. + knun for real numbers k1….kn

k1…kn are called the coefficients of the linear combination.

Question 2

Spans

Answer 2

Let {u1,……,un} be a non empty finite subset of a vector space.
the span is the set of all linear combinations.

Span{u1, . . . , u n} = {k1 u1 + . . . + kn u n | k1, . . . , kn ∈ R}

Question 3

Span Theorem

Answer 3

Let {u1, . . . , u n} be a nonempty finite subset of a vector space V .
Then Span{u1, . . . , u n} is a subspace of V .

Question 4

Spanning Set

Answer 4

Let S be a nonempty finite subset of a vector space V .

S is called a spanning set for V if Span S = V .