Page 433 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(c) A is

If A is an matrix, what are the largest possible value for its rank and the smallest possible value for its nullity?

6.

Hint See Exercise 5.

In each part, use the information in the table to determine whether the linear system is consistent. If so, state the
7. number of parameters in its general solution.

(a) (b) (c) (d) (e) (f) (g)

Size of A 3212202
Rank(A) 3312302
Rank

For each of the matrices in Exercise 7, find the nullity of A, and determine the number of parameters in the general solution

8. of the homogeneous linear system .

What conditions must be satisfied by , , , , and for the overdetermined linear system
9.

to be consistent?
Let

10.

Show that A has rank 2 if and only if one or more of the determinants

are nonzero.
Suppose that A is a matrix whose nullspace is a line through the origin in 3-space. Can the row or column space of A
11. also be a line through the origin? Explain.

Discuss how the rank of A varies with
12.