Question

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) Responses 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. Rows cannot be added together. Rows can only be multiplied by positive numbers.

Answer 1

To solve a system of equations using row operations and convert its augmented matrix to row echelon form, none of the provided statements are true.

Here is clarification on the operations you can perform:

1. Row interchanges are allowed: You can swap rows. Therefore, row 1 does not need to begin with a zero; it can begin with any non-zero entry as long as you apply appropriate row operations.

2. Row addition is allowed: You can add or subtract rows from one another to eliminate variables. Therefore, the statement "Rows cannot be added together" is incorrect.

3. Rows can be multiplied by non-zero numbers: You can multiply rows by any non-zero number, not just positive numbers. Therefore, "Rows can only be multiplied by positive numbers" is false.

Thus, none of the statements are true in the context of solving systems of equations through row operations.