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?

This solution is comprised of a step-wise response which investigates the concepts of matrices, sets and relations. This response is detailed and well presented in a Word document which is attached.

Please provide detailed explanation that verifies response.
Also, please use formal set notation to prove necessity and sufficiency.
If possible, please post response as either a MS Word or PDF file.
Infinite Thanks for your time!

Let R1 and R2 be relations on a set A. represented by the matrices:
M R1 0 1 0 M R2 0 1 0
1 1 1 0 1 1
1 0 0 1 1 1
find the matrices that represent ( show all work)
a) R1 union R2
b) R1 intersection R2
c) R2 º R1 (composition)
d) R1 º R1 (co

One of the problems of storing data in a matrix (a two-dimensional Cartesian structure) is that if not all of the elements are used, there might be quite a waste of space. In order to handle this, we can use a construct called a "sparse matrix", where only the active elements appear. Each such element is accompanied by its two i

Perform the given operation for the following zero-one matrices:
1 0 1 1 1
1 0 0 = 0 1
0 1 1 1 1
Show that
2 3 -1
1 2 1
-1 -1 3
is the inverse of
7 -8 5
-4 5 -3
1 -1 1

2. Use Theorem 5.2.1 to determine which of the following are subspaces of M22.
Thm 5.2.1: If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold.
(a) If u and v are vectors in W, then u + v is in W.
(b) If k is any scalar and u is any vector in W,

See attached file.
Consider the relationship between the matrices A and B, explore the relationship between A and B and matrices representing other linear transformations derived from F and G. Explore 2 examples for example F+G for various and , or the composite function FG/
Check th