High School Finding Bases for Row and Column Spaces

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To find bases for row and column spaces, it is effective to first reduce the matrix to echelon form. The discussion raises the question of whether reduced echelon form can also be used to identify these bases. Testing this approach with a simple three-by-three matrix is suggested to compare results. Ultimately, both echelon forms can yield valid bases for the respective spaces. Understanding the relationship between these forms is crucial for solving related problems effectively.
a1234
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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.
 
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a1234 said:
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.
 
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