What is a Basis: [ Ссылка ]
What is Null Space: [ Ссылка ]

The Column Space of a matrix is the span of the columns of the matrix.
The Null Space of a matrix, A, is the collection of all x vectors that satisfy Ax=0.
Rank is the dimension of the column space
Nullity is the dimension of the null space
Rank of A + Nullity of A = number of columns of A

Video Guide:

How to find basis for Col(A): 0:55
How to find basis for Nul(A): 2:28
What is Rank and Nullity: 7:20
Rank/Nullity Theorem: 8:51

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