Page 363 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Use Theorem 5.2.1 to determine which of the following are subspaces of
2.

(a) all matrices with integer entries
(b) all matrices

where
(c) all matrices A such that

(d) all matrices of the form

(e) all matrices of the form

Use Theorem 5.2.1 to determine which of the following are subspaces of .
3.

(a) all polynomials for which

(b) all polynomials for which

(c) all polynomials for which , , , and are integers

(d) all polynomials of the form , where and are real numbers

Use Theorem 5.2.1 to determine which of the following are subspaces of the space
4.

(a) all f such that for all x

(b) all f such that

(c) all f such that