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Math Help - The elementary transformation of matrix

  1. #1
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    Post The elementary transformation of matrix

    As we know ,there are three different elementary transformations of matrix, they are "change two distinct rows", "multiply a non-zero number to a row of the matrix","add a k times of a row to another row,where k is a number in the field and non-zero".

    Obviously,we can use the last two to get the first elementary transformation("change two distinct rows"), so whether the first elementary transformation is unnecessary?

    Another question is : what is the geometric meaning of these elementary transformations of matrix?
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  2. #2
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    Hi - I would stick my neck out and say it is just because of convenience. So that we can apply them directly without worrying too much about which row to multiply with what and add etc to get an interchange of rows. It could be that these three were most common of the operations required to bring matrices on reduced form.

    Essentially, row operations on given a set of vectors (represented by a matrix), is that you do some linear combination so that the linear span of the resultant set of vectors is same as the starting set of vectors.

    I do not know if there is any geometric meaning to row-operations.

    Will appreciate if anyone can offer more insight here.
    Thanks
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