Multiplying a linear equation through by zero is an acceptable elementary row op.
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Multiplying a linear equation through by zero is not an acceptable elementary row operation. In fact, it is not an elementary row operation at all.
There are three acceptable elementary row operations:
1. Interchanging two rows.
2. Multiplying a row by a nonzero scalar.
3. Adding a multiple of one row to another row.
These operations are used in Gaussian elimination to transform a matrix into row echelon form or reduced row echelon form.
Multiplying a row by zero would result in a row of zeros, which would not change the rank or determinant of the matrix, but it would change the nature of the system of equations that the matrix represents. This is because a row of zeros would correspond to a redundant or inconsistent equation in the system, which would alter the solution set.
Therefore, multiplying a linear equation through by zero is not a valid elementary row operation.
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