Question

Which of the following is NOT an elementary row operation?A. Delete a row of negative numbers Which of the following is NOT an elementary row operation?

A. Delete a row of negative numbers
B. Interchange (swap) two rows
C. Add a multiple of one row to another row
D. Multiply a row by a nonzero constant

Answer 1

The correct answer is A. Delete a row of negative numbers. An elementary row operation is a specific operation that can be performed on the rows of a matrix without changing its solution. The three elementary row operations are interchanging (swapping) two rows, adding a multiple of one row to another row, and multiplying a row by a nonzero constant.

Step-by-step explanation:

The correct answer is A. Delete a row of negative numbers.

An elementary row operation is a specific operation that can be performed on the rows of a matrix without changing its solution. The three elementary row operations are:

1. Interchanging (swapping) two rows: This involves swapping the positions of two rows in a matrix. For example, if we have a matrix with rows R1 and R2, interchanging them results in a new matrix with rows R2 and R1.
2. Adding a multiple of one row to another row: This involves adding a multiple of one row to another row. For example, if we have a matrix with rows R1 and R2, adding 2 times R1 to R2 would result in a new matrix with rows R1 and R1+2R2.
3. Multiplying a row by a nonzero constant: This involves multiplying a row by a nonzero constant. For example, if we have a matrix with rows R1 and R2, multiplying R2 by 3 would result in a new matrix with rows R1 and 3R2.

Deleting a row of negative numbers is not a valid elementary row operation because it does not fall into any of the three defined operations.