We have a variety of theorems about how to create column spaces and row spaces and they
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We have a variety of theorems about how to create column spaces and row spaces and they frequently involve row-reducing a matrix. Here is a procedure that some try to use to get a column space. Begin with an m n matrix A and row-reduce to a matrix B with columns B1, B2, B3, . . . , Bn. Then form the column space of A as
C(A) = ({B1, B2, B3, . . . , Bn}) = C(B)
This is not a legitimate procedure, and therefore is not a theorem. Construct an example to show that the procedure will not in general create the column space of A.
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Begin with a matrix A of any size that does not have any zero rows but which when rowreduced to B y...View the full answer
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