Finding Bases for Row and Column Spaces

[a1234]

I'm doing problems on finding row and column spaces. My textbook tells me to find the echelon form of the matrix, and then to identify the bases. My question is, can I reduce the matrix to reduced echelon form to get the bases? I have the same question about bases for the solution space.

 

[Ray Vickson]

I'm doing problems on finding row and column spaces. My textbook tells me to find the echelon form of the matrix, and then to identify the bases. My question is, can I reduce the matrix to reduced echelon form to get the bases? I have the same question about bases for the solution space.

Why not? Have you tried it for yourself? Just take a simple example involving, for example, the row space for a particular three by three matrix, then try both reductions and see what you get.