Course: MIT OCW 18.06 Intro to Linear Algebra by Strang 4th edt.(adsbygoogle = window.adsbygoogle || []).push({});

Question: if a_{3,3}is 7, and the third pivot is 5, if we change a_{3,3}to be 11, then the third pivot becomes _________. If you change the a_{3,3}to ________ then there is no third pivot.

At first I thought a_{3,3}had to be the actual third pivot (yes?no?). Definitions for what a pivot is are muddled throughout the resources I've used, but the most solid definition I've found is from the course text itself and it says (to paraphrase):

1 >> The pivots are on the diagonal of the upper triangular matrix after elimination is complete whereby back substitution may begin

To not paraphrase it also says

2 >> "pivot = 1st nonzero in the row that does the elimination"

From the first definition, shouldn't a_{3,3}be the pivot?

If not, then perhaps there is a 5 leading the third row...ok. But then if we changed the 7 to an 11, that would be by multiplying all the elements of the row by a constant multiple, and the answer in the solutions guide says that changing a_{3,3}from 7 to 11 changes the pivot from 5 to 9...

I am clearly lacking some fundamental understanding in what a pivot is. Can someone help?

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# I need help understanding pivots

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