Page 437 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Chapter 5

Supplementary Exercises

In each part, the solution space is a subspace of and so must be a line through the origin, a plane through the origin, all
1. of , or the origin only. For each system, determine which is the case. If the subspace is a plane, find an equation for it,

and if it is a line, find parametric equations.
(a)
(b)

(c)

(d)

For what values of s is the solution space of
2.

the origin only, a line through the origin, a plane through the origin, or all of ?

3. as a linear combination of (4, 1, 1) and (0,−1, 2).
(a) Express

(b) Express as a linear combination of (3, −1, 2) and (1, 4, 1).

(c) Express as a linear combination of three nonzero vectors.

Let W be the space spanned by and .
4.