
NY Form 39-1 2009-2025 free printable template
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- Hi I'm Jen fromCalcworkshop and in this video we're going to learn about the most important technique in all of linear algebra row reduction So either the form off or Row Echelon Form or Reduced Row Echelon Form or REEF Both of these techniques are pivotal to your success in linear algebra We're going to walk through bunch of examples to make sure that you are successful in understanding this important concept So check it out Alright so let's look at the two forms of row reduction The first one is called Row Echelon Form Some people refer to ITAs just Echelon Form and others refer to ITAs Gauss Elimination since Gauss was the first to have actually come up with this idea We abbreviate and narrow Echelon Form is REF which is referred to arrow Echelon Form Refine Gauss Elimination Here's the idea We're going to take a system and we again we know we like the identity matrix That's our main guy that we like 'cause ones and zeros are the easiest What we want to do is to using techniques that we're gonna talk about in a second is to reduce our matrix down so that we get ones along the main diagonal if you can see that ones going along the main diagonal and if you see in the lower triangle we're creating this lower triangle of all zeros So again the objective into create an upper triangle with just numbers and the lower triangle has all zeros with ones along the main diagonal That is our objective So what we're doing isle're taking a system we're reducing it Downs that we get one's down the main diagonalzeros in the lower triangle Now this is a square matrix meaning we have three rows three columns, so we know we're going to get a main diagonal If you look here it'snot a square matrix We have four rows and only three columns This is a four by three matrices so there really isn't again diagonal to speak of We can kinda tell it'got that diagonal feel, but it's not a nice cut symmetry that we can see in the first one and that's okay We're still going to try our best to get this main diagonal if we can kinda fudge it and say okay I know it's not square I know I don't have a main diagonal going all the way down but again what I'm looking for is to get one's coming down diagonally zeros in the lower triangle Here's the big key So we know that we want to get this lower triangle of zeros For REF here's what's gotta happen you get your ones and everything below the one must be a zero Everything below the one in each column must be a zero So that is the main objective for REF Now what are these little asterisks These asterisks represent any number we want them to be; we don't really care because what we'll be able to do is do back-substitutionto find our answer, and we're seen how to do substitution; we've been doing it since Algebra 1 So the asterisks represent any number What we want to do is ketones along a diagonal zeros below any of the ones That's for REF Row EchelonForm or Gauss Elimination Now why don't we like this one as much as the second one...
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