Question

a. Is the statement​ "Every elementary row operation is​ reversible" true or​ false? Explain. A. ​True, because interchanging can be reversed by​ scaling, and scaling can be reversed by replacement. B. ​False, because only scaling and interchanging are reversible row operations. C. ​True, because​ replacement, interchanging, and scaling are all reversible. D. ​False, because only interchanging is a reversible row operation.

Answer 1

Answer: C. ​True, because​ replacement, interchanging, and scaling are all reversible.

Step-by-step explanation:

Elementary operations in a matrix are defined as :

• Operations in arithmetic ( such as add , subtract, multiply, divide).
• They are of two kinds : Elementary row operations and  elementary column operations.

Every elementary row operation is​ reversible.

• If we add row to the another row  then we can reverse it by subtracting the first row from the other on the next step
• If we interchange a row by another then we can again interchange it on the next step.
• If we we multiply a constant on a row , we can reverse it by multiplying the inverse of the constant to the row on the next step.

Therefore , the correct answer is C. ​True, because​ replacement, interchanging, and scaling are all reversible.