12
QuizMultiple Choice

Matrices and Row Operations — Quiz

Question 12 • Advanced Algebra: Concepts and Connections

Which operation can be used with the augmented matrix? the 3 by 4 matrix, row 1, column 1, 3 column 2, negative 2 column 3, 1 column 4, 15 row 2, column 1, 1 column 2, 5 column 3, 8 column 4, 15 row 3, column 1, negative 2 column 2, negative 1 column 3, 3 column 4, 1

Answer
A
Add row 2 and column 3 .
B
Multiply row 3 by 0 .
C
Multiply row 2 by negative 1 and add it to row 3 .
D
Switch column 1 and column 2 .

Explanation

Elementary row operations allow you to replace one row with itself plus a multiple of another row. Choice D replaces row 3 with row 3 plus (−1) times row 2, which is a valid row operation. Adding a row to a column or switching columns is not an elementary row operation, and multiplying a row by 0 is not allowed because it destroys information.

AI-written and checked against the verified answer.

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