Math 220 Assignment

October 22, 2001

Due Wednesday, October 24

Let M be an m \times n matrix, and let f denote the corresponding linear function from R^{n} to R^{m}.

1. Which of the following sets related to M are preserved under arbitrary (finite) sequences of elementary row operations?

   1. The set of linear combinations of the columns of M.

   2. The set of linear combinations of the rows of M.

   3. The set of linear relations among the columns of M.

   4. The set of linear relations among the rows of M.

2. Which of the sets enumerated in the previous exercise have straightforward interpretations in terms of the linear map f ?

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