Carnegie Mellon

21-241 Matrix Algebra
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Assignments: Week #4

Reading:
  • Monday: Section 6.4 all, and Section 3.1 pp. 147-151.Exam #1. (Also see posted notes on Vector Spaces, section 3.4 Linear Transformations and Matrices.)
  • Wednesday: Section 3.1 pp. pp. 138-145, 150-152 and Section 3.2. (Also see posted notes on Matrix Algebra, section 4.1 Matrix Operations.)
  • Friday: Section 3.1 pp. 151-156 and Section 160-166. (Also see posted notes on Matrix Algebra, section 4.2 Representations of Matrix Multiplication.)

Exercises:
  • Wednesday: WeBWorK - Week #4 Online Homework.
  • Friday:
    1. 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.
    2. 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)).
    3. 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.
    4. Let V and W be vector spaces and T:V->W a linear transformation. Let V0 denote the set V0={v in V: T(v)=0W}. Show that V0 is a vector space (using the same addition and scalar multiplication as in V). [Note: since the vectors in V0 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:

  1. Your name (on every page if you ignore #4.),
  2. Your class section,
  3. The names of those students with whom you have collaborated,
  4. a staple.