Multiplying a particular row of a matrix by 0 will result in a row of all zeros. This operation is known as row scaling or row multiplication. If this row corresponds to an equation in a system of linear equations, it means that the equation becomes a trivial equation of the form 0 = 0.
This row of zeros does not affect the other rows in the system, since multiplying a row by 0 does not change the values of the other rows. However, it does affect the solution of the system. If the row of zeros corresponds to a variable in the system, it means that this variable can take any value and does not affect the solution of the system. This variable is called a free variable.
In general, row scaling does not change the solution of a system of linear equations, since it is an elementary row operation that can be reversed by dividing the row by 0 (which is undefined) or by multiplying the row by a nonzero constant. However, row scaling can be useful in solving systems of linear equations, since it can simplify the system and make it easier to solve.