which of the following sets of data would you likely represent with a square matrix?\na shoe salesperson…

which of the following sets of data would you likely represent with a square matrix?\na shoe salesperson wants to use an augmented matrix to represent the quantity of childrens shoes and adult shoes sold at his store for two days.\na racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.\na student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.\na teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.

which of the following sets of data would you likely represent with a square matrix?\na shoe salesperson wants to use an augmented matrix to represent the quantity of childrens shoes and adult shoes sold at his store for two days.\na racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.\na student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.\na teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.

Answer

Explanation:

Step1: Recall square - matrix definition

A square matrix has the same number of rows and columns.

Step2: Analyze option A

For the shoe - salesperson, we have 2 types of shoes (children's and adult's) and 2 days. The augmented matrix would be (2\times2) (a square matrix). But let's check other options.

Step3: Analyze option B

In a racquetball club tournament where each member plays every other member, if there are (n) members, the matrix representing the scores will be (n\times n) (a square matrix).

Step4: Analyze option C

A student writing a coefficient matrix for a linear system with 2 equations and 3 unknowns will have a (2\times3) matrix, which is not square.

Step5: Analyze option D

A teacher writing an augmented matrix for a linear system with 4 equations and 4 unknowns. The augmented matrix will be (4\times(4 + 1)=4\times5) (not square), but the coefficient matrix will be (4\times4) (square).

Since options A, B, and D can be represented by square matrices.

Answer:

A. A shoe salesperson wants to use an augmented matrix to represent the quantity of children’s shoes and adult shoes sold at his store for two days. B. A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix. D. A teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.