1. Swap two rows: Swap two rows in the matrix. This transformation does not change the rank of the matrix. If the matrix is reversible, its inverse matrix can be obtained through a series of row exchanges. When two rows are exchanged, it is necessary to pay attention to maintaining the equivalence relationship of matrices. Only when there are elements crossing between two rows can they be exchanged. Otherwise, this transformation will cause the matrix to lose its meaning.

2. Eliminate elements in a row: select an element in a row, multiply it by a non-zero constant, and add it to the row where another element is located, so that the element is eliminated to zero. This transformation is called line elimination. It does not change the rank of the matrix. In the online elimination method, attention should be paid to selecting appropriate elements and constants.

3. Eliminate the relationship between two rows: select the corresponding elements in two rows to make them equal. Specifically, if the corresponding elements in two rows are proportional, a series of rows can be used to eliminate the elements and make all the elements in two rows equal. This transformation is called line simplification.

In the elementary row transformation of matrix, we should pay attention to the following points:

1. Select the appropriate elementary line transformation: according to the specific problems and goals, select the appropriate elementary line transformation. For example, if you need an inverse matrix of a matrix, you should simplify the matrix into the simplest form by row elimination, and then find the inverse matrix according to the definition.

2. Maintain the legitimacy and effectiveness of the transformation: When performing elementary line transformation, it is necessary to ensure the legitimacy and effectiveness of the transformation. For example, two rows in a matrix cannot be interchanged unless an element passes through them.

3. Pay attention to the order and mode of transformation: the order and mode of elementary line transformation may affect the final result. Therefore, it is necessary to carefully choose the order and mode of transformation to achieve the best effect.

4. Avoid over-transformation: Over-transformation may cause the matrix to be meaningless or unsolvable. For example, if there is no non-zero element in a row, it can no longer be eliminated.

5. Pay attention to the handling of special circumstances: for some special circumstances, special handling is needed. For example, for some irreversible matrices, it is necessary to find their approximate solutions or least square solutions through some special elementary row transformations.