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(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}.
This theorem relates all of the major topics we have studied thus far.
Exercise Set 6.2
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In each part, determine whether the given vectors are orthogonal with respect to the Euclidean inner product.
1.
(a) ,
(b) ,
(c) ,
(d) ,
(e) ,
(f) ,
Do there exist scalars k, l such that the vectors , , and are mutually orthogonal with
2. respect to the Euclidean inner product?
and . If , what is k?
Let have the Euclidean inner product. Let
3.
