Page 403 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

33. matrix A, explain in words why the set , must be linearly
(a) For a

dependent if the ten matrices are distinct.

(b) State a corresponding result for an matrix A.

State the two parts of Theorem 5.4.2 in contrapositive form. [See Exercise 34 of Section 1.4.]
34.

35. can be viewed as a linear system of one equation in n
(a) The equation

unknowns. Make a conjecture about the dimension of its solution space.

(b) Confirm your conjecture by finding a basis.

36. is a subspace of .
(a) Show that the set W of polynomials in such that

(b) Make a conjecture about the dimension of W.

(c) Confirm your conjecture by finding a basis for W.

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