Homework SourseNeed some help 1 Let A be an n x n matrix with real numbers
Need some help. 1. Let A be an n x n matrix with real numbers as entries. Define the inverse of A 2. Let A = the set of courses required for your degree. Let the relation R be defined on A by course x is related to course y if course x is a prerequisite of course y. Explain why this relation is a antisymmetric relation. Is this relation a transitive relation? Explain 3. Assume that your job as a senior on campus is to assign students to dorm rooms. Assume you have nine students to assign to rooms and the rooms are a quad, a triple and a double. How many ways can you make the assignments?
Solution
1) Inverse of A (if determinant A is not zero) is the matrix B such that
AB = Id, where Id is the identity matrix of size n.
or A = (detA)-1 B, where B is the adjoint of A
2) If xRy and yRx, then x is a prerequisite for y and y is a prerequisite for x,
This is possible iff x=y .
So this is anti-symmetric.
This is transitive. If xRy and yRz, in order to study z , x is a prerequisite
(3) The number of assignments = 9C4 x5C3x2C2
= 1260
