Page 473 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(c) and using the inner product given in Example 8 of Section 6.1

Let W be the line in with equation . Find an equation for .
14.

15. . Find parametric equations for .
(a) Let W be the plane in with equation

(b) Let W be the line in with parametric equations

Find an equation for .
(c) Let W be the intersection of the two planes

in . Find an equation for .
Let
16.

(a) Find bases for the row space and nullspace of A.

(b) Verify that every vector in the row space is orthogonal to every vector in the nullspace (as guaranteed by Theorem
6.2.6a).

Let A be the matrix in Exercise 16.
17.

(a) Find bases for the column space of A and nullspace of .

(b) Verify that every vector in the column space of A is orthogonal to every vector in the nullspace of (as
guaranteed by Theorem 6.2.6b).

Find a basis for the orthogonal complement of the subspace of spanned by the vectors.
18.

(a) , ,