Matrices — Test

Question 14 • Algebra II

Which of the following sets of data would you likely represent with a square matrix?

Answer

A teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.

A student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.

A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.

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.

Explanation

A square matrix has the same number of rows and columns. In the tournament, each member plays every other member, so the score table can use one row and one column for each member, giving equal numbers of rows and columns. Choice B’s augmented matrix has four rows but five columns (four unknowns plus the constants), so it is not square; choices C and D also have unequal row and column counts.

AI-written and checked against the verified answer.

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