One suggest exercise

[Valerón]

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."

[Valerón]

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]

Hi Valeron,

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

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

Rob