Assignments: Week #4
Reading: 
 Monday: Section 6.4 all, and Section 3.1 pp. 147151.Exam #1. (Also see posted notes on Vector Spaces, section 3.4 Linear Transformations and Matrices.)

Wednesday: Section 3.1 pp. pp. 138145, 150152 and Section 3.2.
(Also see posted notes on Matrix Algebra, section 4.1 Matrix Operations.)

Friday: Section 3.1 pp. 151156 and Section 160166. (Also see posted notes on Matrix Algebra, section 4.2 Representations of Matrix Multiplication.)

Exercises:


Wednesday: WeBWorK  Week #4 Online Homework.

Friday:
 Prove Theorem 6.1 part (a) on page 433 in Poole by showing that 0v satisfies axiom 4 in the definition of a vector space.
 Section 6.4 #21: Prove Theorem 6.14 part (b) on p. 475 in Poole. Make a clear distinction between the additive inverse, v, and the scalar product, (1)v, even though they are equal (by Theorem 6.1(c)).
 For the system of equations in problem 2.1.16,
(a) draw a diagram that shows the row picture for the system, and (b) draw a diagram that shows the column picture.

Let V and W be vector spaces and T:V>W a linear transformation. Let V_{0} denote the set V_{0}={v in V: T(v)=0_{W}}. Show that V_{0} is a vector space (using the same addition and scalar multiplication as in V). [Note: since the vectors in V_{0} are all in the vector space V, some of the axioms are very easy to prove.]


Homework assignments may be turned in before or after class on the due day, or
may
be placed in your TA's mailbox before 3:20pm on that day. The TA's
mailboxes are in the Math Department office, WEH 6113.
Please make sure your homework
includes the following:
 Your name (on every page if you ignore #4.),
 Your class section,
 The names of those students with whom you have collaborated,
 a staple.