One suggest exercise

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Mar 7, 2009, 7:28:43 AM3/7/09
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I've read section LDS in chapter V, when I figure the concepts in my
mind, something haven't been mentioned raise. Yet I'm not sure if a
self-learner is suitable to suggest exercise, I'd like to leave it
here for discussion.

Here it is:
"According to Theorem BS, for any vector set S, we know one can
"safely" eliminate any column vectors corresponding to free-variable
in row-reduced echelon form of the matrix consist of all the vectors
from the set, if there exist any free-variable, without destruct <S>.
How about the vectors corresponding to pivot column? Can them be
"safely" removed? If not, what's the restriction? Or is there any
determination to sentence a pivot column to be redundancy? Prove your
idea or disprove mine."


Mar 7, 2009, 7:37:56 AM3/7/09
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I'd like to add one more interesting hint to this exercise.

"If you make it, try do it again without consulting theorem DLDS or
suppose you don't know this theorem"

Rob Beezer

Mar 21, 2009, 12:11:52 AM3/21/09
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Hi Valeron,

I think even with or without DLDS this could be a thought-provoking

See Example RSC5 in the text, I think it has all the ideas you are
trying to confront with this exercise.

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