Answers Advanced Algebra Concepts and Connections Matrices and Their Inverses — QuizQuestion 4

4

QuizMultiple Choice

Matrices and Their Inverses — Quiz

Question 4 • Advanced Algebra: Concepts and Connections

Which of the following matrices has an inverse?

Answer

A

the 1 by 3 row matrix column 1 4 column 2 negative 2 column 3 1

B

the 2 by 2 matrix, row 1, column 1, 6 column 2, negative 9 row 2, column 1, 2 column 2, 1

C

the 2 by 1 column matrix row 1 negative 6 row 2 3

D

the 2 by 3 matrix, row 1, column 1, negative 3 column 2, 5 column 3, 1 row 2, column 1, 4 column 2, negative 6 column 3, 0

Explanation

A matrix can have an inverse only if it is square, so choices A, B, and D cannot have inverses. Choice C is a 2 by 2 matrix, and its determinant is 6(1) − (−9)(2) = 24. Since the determinant is not zero, the matrix is invertible.

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