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Closed under addition and scalar multiplication.
- Rn is a subspace of itself.
- Zero subspace is a subspace of Rn--set 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.
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.
set of Nul A of all solutions of the homogeneous equation Ax = 0
Nul A is a subspace of Rn.
- The set of solutions of a system of Ax = 0 is also a subspace of Rn.
a linearly independent set in H that spans H
Row reduce Ax=0, put into vector equation form, and the vectors are the basis
rows with pivots in row reduced matrix