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Subspace
Closed under addition and scalar multiplication.
 Rn is a subspace of itself.
 Zero subspace is a subspace of Rnset consisting of only the zero vector in Rn.
 The zero vector is in H
 For each u and v in H, the sum u + v is in H
 For each u in H and each scalar c, the vector cu is in H.

Column Space
the set of Col A of all linear combinations of the columns of A
pivot columns of A (not row reduced) form basis for column space of A.

Null Space
set of Nul A of all solutions of the homogeneous equation A x = 0
 Nul A is a subspace of Rn.
 The set of solutions of a system of Ax = 0 is also a subspace of Rn.

Basis
a linearly independent set in H that spans H
Row reduce Ax=0, put into vector equation form, and the vectors are the basis

Row Space
rows with pivots in row reduced matrix

