Introduction to Matrices — Quiz

Question 12 • Advanced Algebra: Concepts and Connections

Which of the following is a diagonal matrix?

Answer

the 3 by 3 matrix, row 1, column 1, 2 column 2, 0 column 3, 0 row 2, column 1, 0 column 2, negative 42 column 3, 0 row 3, column 1, 0 column 2, 16 column 3, negative 7 point 5

the 3 by 3 matrix, row 1, column 1, 0 column 2, 0 column 3, 7 point 5 row 2, column 1, 0 column 2, negative 22 column 3, 0 row 3, column 1, 5 column 2, 0 column 3, 0

the 3 by 3 matrix, row 1, column 1, negative 1 column 2, 0 column 3, 0 row 2, column 1, 0 column 2, negative 22 column 3, 0 row 3, column 1, 0 column 2, 0 column 3, 7 point 5

the 3 by 3 matrix, row 1, column 1, 0 column 2, 3 point 5 column 3, negative 18 row 2, column 1, 1 column 2, 0 column 3, 9 row 3, column 1, 6 column 2, negative 4 column 3, 0

Explanation

A diagonal matrix has zeros in every position off the main diagonal, while its diagonal entries may be any numbers. Choice A has diagonal entries −1, −22, and 7.5, and all other entries are 0. The other choices each have at least one nonzero entry off the main diagonal.

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