MIT18.06 Linear Algebra (9)

lec9

Independent

no combination give a zero vector (expect $0$ ).

If columns of $A$ are independent, $N(A) = {0}$ .

Span

vectors span a space means the space consists of all combinations of those vectors.

Basis

Basis for a space is vectors with 2 properties:

• They are independent.
• They span the pace.

Every basis of the space have the same number of vectors. i.e. the dimension.

$\dim N(A) = n-rank(A)$