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Proof TIME! yey

  1. Sep 29, 2004 #1
    Proof TIME! yey....

    ok well im supposed to prove the following...
    Let A be m x n matrix with R as it rref. Let C be the matrix whose columns are all the pivot columns of A (in order), and let S be the matrix obtained by deleting the zero rows, if any, from R.
    a) Show that the matrix product CS is defined
    b) Determine the matrix CS, and justify your answer.

    a)the matrix C will have dimmensions m x rank A and S will have dimmesions S rank A x n because for ever pivot column it takes a row space therefore the number of rows in S must be equal to rank A.

    and the part i need some help with!!
    b) i realize that CS = A, and C is linearly indepent set of the orginal matrix, and u can create all the other columns of A by a linear combination of columns of C, and S has all the scalar multiplies to do so... the reason this works is what i have to explain...any ideas?
  2. jcsd
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