Math410 (Bayly) Homework 3 (due Friday 29 September)

Recall I had you do problems 1.8.1 (a, b, d) and 1.8.2 (a, b, c, d) out of section 1.8 in HW 1,2. Look at them again (and do more if you’re not sure how the process goes). If they have infinitely many solutions, find the min length solution. If there are no solutions, find the least squares approximate solution. If the LS approx is nonunique, find the min length least squares solution.

From pages 127-8 do 2.6.5 and 2.6.11 (you don’t have to prove the general statement, part (d), unless you are seriously motivated to do so).

On page 311 do 6.2.2 and 6.2.4.

TEAM RANKING:

Teams A, B, C, and D play a series of games on successive weekends.

On opening weekend A visits B and wins by 3 (game a), and C visits D and loses by 4 (game b). Draw the network representing the games so far, and say what you can tell so far about the relative winning potentials of the teams.

On the second weekend D visits B and wins by 2 (game c). Redraw the network. Is there a consistent ranking for all the teams? If not, find an approximation*.

On the third weekend B visits C and wins by 2 (game d). Redraw the network. Is there a consistent ranking for all teams? If not, find an approximation*.

On the fourth weekend A visits C and loses by 2 (game e). Redraw the network. Is there a consistent ranking for all teams? If not, find an approximation*.

*Use the least squares approximate solution to EW = D.