Multiplying a linear equation through by zero is an acceptable elementary row op.
No, multiplying a linear equation through by zero is not an acceptable elementary row operation
No, multiplying a linear equation through by zero is not an acceptable elementary row operation. In fact, it is an invalid operation.
Elementary row operations in linear algebra are used to manipulate and transform a system of linear equations without changing the solutions. The three acceptable elementary row operations are:
1. Scaling a row: Multiply all elements of a row by a non-zero constant.
2. Swapping rows: Interchange the positions of two rows.
3. Adding a multiple of one row to another row: Multiply one row by a constant, and then add the resulting row to another row.
These operations ensure that the operations done to rows will not alter the solutions of the system.
However, multiplying a linear equation through by zero violates the fundamental idea of elementary row operations. If you multiply an equation by zero, all the terms on both sides of the equation become zero. As a result, you end up with an equation that does not provide any useful information about the solutions of the system. It essentially transforms the equation into the trivial equation 0 = 0, which holds true for any values of the variables. Therefore, multiplying a linear equation through by zero is not a valid operation and should not be performed.
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