Answer to Question #24236 in Linear Algebra for Adam J
Each elementary row operation can be regarded as a multiplication by the matrix of this operation. It can be easily seen that this matrix is invertible (simply because each elementary row operation is obviously invertible). We know that multiplication by an invertible matrix does not change the rank of the initial matrix. Thus, a row operation preserves the rank.
Answer:& row operations preserve the linear independence of rows as well as the linear independence of columns.
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