Matrices, Sets and Relations

question

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: Please view the attachment for the rest of the question.

Questions:(a) Interpret the above matrices with respect to the above relations.(b) Compute M_SoR, 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?

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 =

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 =
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
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