Page 506 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(f) has exactly one solution for every matrix b.
(g) .
(h) The range of is .
(i) is one-to-one.
(j) The column vectors of A are linearly independent.
(k) The row vectors of A are linearly independent.
(l) The column vectors of A span .
(m) The row vectors of A span .
(n) The column vectors of A form a basis for .
(o) The row vectors of A form a basis for .
(p) A has rank n.
(q) A has nullity 0.
(r) The orthogonal complement of the nullspace of A is .
(s) The orthogonal complement of the row space of A is {0}.
(t) is invertible.

This theorem relates all of the major topics we have studied thus far.

Exercise Set 6.4

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