Linear Independence and Basis

Question 1

What is a spanning set for W?

Answer 1

If a subspace W of V is expressible as W = Span(v1, v2, ….., vk) then {v1, ….., vk} is a spanning set of W (set of all linear combinations)

Question 2

What is the row space?

Answer 2

Subspace of Fm that can be spanned by these rows

Question 3

What is the column space?

Answer 3

Subspace of Fn that can be spanned by these columns

Question 4

Linear independence

Answer 4

If the only solution to
a1v1 + a2v2 + …… + akvk 0 is
a1 = a2 = a3 = ……. = ak = 0

Question 5

If two vectors in the set can be written as linear combinations of the others then the set is

Answer 5

Linear dependent