Matrices, Sets and Relations

Statexpert
question.doc

Let:

D = days of the week {M, T, W, R, F},

E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University U = {Courses the tutoring center needs tutors for}

= {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C1), Computers II (C2), Precalculus (P)}.

We define the relation R from D into E by d R e, if employee e is scheduled to work on day d. We also define S from E into U by e r u, if employee e is capable of tutoring students in course u. If:

MR =

image1.wmf

BJK

1 0 1

M

0 1 1

T

1 0 1

0 1 0

1 1 0

W

R

F

éù

êú

êú

êú

êú

êú

êú

ëû

and MS =
image2.wmf

12

I II III C C P

B0 1 1 0 0 1

J1 1 0 1 0 1

K0 1 0 0 1 1

éù

êú

êú

êú

ëû

(a) Interpret the above matrices with respect to the above relations.

(b) Compute

image3.wmf

SR

M

o

, and use this matrix to determine which courses will have tutors available on which days.

(c) Multiply the above matrices using regular arithmetic. Can you interpret this result?

_1194172502.unknown

_1194172503.unknown

_1194172501.unknown