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Math Help - Column Space

  1. #1
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    Column Space

    I know to work out the column space of a matrix you should put it into row echelon form and then look at which columns have a pivot- a basis for the column space is then the corresponding columns of the original matrix. Is it also valid to transpose the original matrix work out a basis for the row space by performing row reduction and then viewing these rows as columns?
    Thanks!
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  2. #2
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    Re: Column Space

    Unlike the column space, the row space is not affected by performing row reduction.
    So just do the row reduction, and the non-zero rows in the reduced form give you your basis.
    Thanks from emakarov
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  3. #3
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    Re: Column Space

    Quote Originally Posted by Chad950 View Post
    Is it also valid to transpose the original matrix work out a basis for the row space by performing row reduction and then viewing these rows as columns?
    Yes, you can find the column space by transposing the matrix, performing row reduction and taking the nonzero rows as basis.
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