Is the statement Every elementary row operation is reversible true or false? Explain.
True, because replacement, interchanging, and scaling are all reversible.
The statement Every elementary row operation is reversible is true.
This is because elementary row operations involve adding, subtracting, or multiplying a row by a constant and these operations can be undone or reversed by performing the opposite operation.
For example, if we add two rows together, we can reverse this operation by subtracting the same two rows. If we multiply a row by a constant, we can reverse the operation by multiplying by the reciprocal of that constant.
Therefore, every elementary row operation can be reversed and this property is important in the process of row reduction and finding solutions to linear systems.
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