If E is an
elementary matrix and A is an
matrix, then the subspace spanned by the rows of A is the same as the subspace spanned by the rows of EA.

Question

If E is an 
  elementary matrix and A is an 
  matrix, then the subspace spanned by the rows of A is the same as the subspace spanned by the rows of EA.

Quizplus · Accepted Answer

This is because elementary matrices represent elementary row operations, which do not change the row space of a matrix. Therefore, applying an elementary matrix to a matrix does not change the subspace spanned by its rows.

If E Is an