Graph Theory Pretest

Attempt to complete the following test in under 60 minutes. After you complete the test, check the Graph Theory Pretest Solutions and evaluate how many questions you answered correctly.

1. How many different ways can you rearrange 10 distinct objects in a row?

Question 2

2. Given the following mxn = 5x7 matrix:

(1)

\begin{align} A = \begin{bmatrix} 2 & 3 & -1 & 0 & 5 & 2 & 9 \\ 4 & 6 & 2 & -7 & 11 & n & 0\\ 9 & k & -22 & 1 & 0 & 4 & 4\\ 9 & 3 & 2 & 0 & 2 & 4 & -1\\ -11 & 2 & 0 & 5 & 2n & 0 & 3 \end{bmatrix} \end{align}

• A) What is the matrix 2A?

• B) Is the determinant of this matrix defined? Why or why not?

• C) Given T as an r x s matrix, for what values of r and s is the matrix product AT defined?

• D) Determine the value of $\sum_{k=1}^{n} a_{3n}$.

• E) Determine the value of $\sum_{k=1}^{m} a_{6m}$.

• F) Define what it is meant for a square matrix B to be symmetric.

2. How many vertices, edges, and faces does a pentagonal prism contain?