Page 364 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(d) all constant functions , where and are real numbers
(e) all f of the form

Use Theorem 5.2.1 to determine which of the following are subspaces of .
5.

(a) all matrices A such that

(b) all matrices A such that

(c) all matrices A such that the linear system has only the trivial solution

(d) all matrices A such that for a fixed matrix B

Determine whether the solution space of the system is a line through the origin, a plane through the origin, or the

6. origin only. If it is a plane, find an equation for it; if it is a line, find parametric equations for it.

(a)

(b)

(c)

(d)

(e)

(f)