Final answer:
The statement that every elementary row operation is reversible is true because each type such as swapping rows, multiplying by a scalar, or adding a multiple of one row to another has a corresponding inverse operation.
Step-by-step explanation:
The statement 'Every elementary row operation is reversible' is true. In linear algebra, elementary row operations are used in methods such as Gauss-Jordan elimination to solve systems of equations. There are three types of elementary row operations: swapping two rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another row.
Each of these operations has a corresponding inverse operation that can restore the original matrix. For instance, if you swap rows 1 and 2, you can reverse this by swapping them back. If you multiply a row by a scalar, you can divide it by the same scalar to revert. Lastly, if you add a multiple of one row to a second row, you can subtract the original multiple from the second row to undo the change.
For example, if we multiply a row by 2, we can divide the row by 2 to undo the operation and retrieve the original matrix. Similarly, if we add a multiple of one row to another, we can subtract the same multiple of one row to reverse the operation.