Which of the following is true to solve a system of equations using row operations to convert its augmented matrix to row echelon form?(1 point)

Question

Responses

Rows can only be multiplied by positive numbers.
Rows can only be multiplied by positive numbers.

Row 1 must begin with a zero.
Row 1 must begin with a zero.

Row 2 must begin with a zero.
Row 2 must begin with a zero.

Rows cannot be added together.

Answer 1

None of the statements provided are true for solving a system of equations using row operations to convert its augmented matrix to row echelon form.

To clarify:

1. Rows can only be multiplied by positive numbers. - This is false. Rows can be multiplied by any non-zero number, including negative numbers.

2. Row 1 must begin with a zero. - This is false. Row 1 typically starts with a leading coefficient, which is often a non-zero number.

3. Row 2 must begin with a zero. - This is also false. Row 2 may have a leading coefficient that is non-zero, depending on the specifics of the system of equations.

4. Rows cannot be added together. - This is false as well. Adding rows together is a fundamental operation in row reduction.

To summarize, none of the statements are correct in the context of performing row operations to reach row echelon form.