Question

which of the following sets of data would you likely represent with a square matrix? check all that apply. a travel company wants to use a matrix to represent the number of flights of several different airlines to several different cities. a tennis club has a tournament in which each member plays every other member, and represents the scores in a matrix. a coefficient matrix is used to represent a linear system with 3 equations and 3 unknowns. the augmented matrix is used to represent a linear system with 3 equations and 3 unknowns.

Explanation:

1. In the case of the travel company, if there are $m$ airlines and $n$ cities, the matrix representing the number of flights will be an $m\times n$ matrix which is not necessarily square ($m$ may not equal $n$).
2. For the tennis - club tournament, if there are $n$ members, and we represent the scores where the rows and columns are both labeled by members, the matrix will be an $n\times n$ square matrix since each member plays every other member.
3. A coefficient matrix for a linear system with $n$ equations and $n$ unknowns is an $n\times n$ square matrix. Here, $n = 3$, so it's a square matrix.
4. An augmented matrix for a linear system with $n$ equations and $n$ unknowns has an extra column (for the constants on the right - hand side of the equations), so it is an $n\times(n + 1)$ matrix and is not square.

Answer:

B. A tennis club has a tournament in which each member plays every other member, and represents the scores in a matrix.
C. A coefficient matrix is used to represent a linear system with 3 equations and 3 unknowns.