/sci/ - Science & Math

What do system of linear equations mean geometrically?

>>10495219
I know that system eqn represent planes and gauss Jordan elimination is used to find the solution of the system when in echelon form, but what does it mean geometrically to apply the transforms/ operations on columns and rows of a 3*3 matrix and how does it change.

>>10495212
>that picture
Didn't anyone ever teach you it's a bad idea to show your identity on 4chan?

>>10495224
>Identity
I get it
Now tell me what does it mean to convert a 3 by 3 into that thing by GJ elimination

>>10495224
*ba dum tss

>>10495212
you can use it to find the basis of a set of vectors

>>10495212
in each step you replace the standard basis by some its linear combination, until you end up with a basis in which your object has a very simple form (depends on what the matrix represents in the first place)

>>10495278
how does that work geometrically

>>10495212
Do you know the difference between a matrix and a linear operator? There lies your answer.

>>10495212
Think about it, if you have a pivot in every row that means that the particular matrix spans r^n of a mxn matrix which means we can generate any type of line, plane ect.. in the dimension of r^n it also means we can generate any plane line ect.. in any dimension less than n. You will later learn more about dimensions and what a dimension means in math in linear algebra and further in your abstract algebra course. https://www.youtube.com/watch?v=k7RM-ot2NWY&index=3&list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B This video shows a very good animation about it.

>>10495222
I have to say that I don't really like this particular geometric explanation, but given your knowledge, I think this is exactly what you're looking for:
https://www.youtube.com/watch?v=bnC848ie16Q

>>10495219
They can be interpreted as n-dimensional planes and the solutions as sub-planes.
I guess it boils down to figuring out what adding the equations of two planes does.

>>10495212
You guys are all terrorists.
You are all asking how to input rituals. With a corresponding operation chart.

All of the row reduction techniques produce equivalent matrices which would have the same geometry as the original matrix.

>>10495212
I heard if you track Obama’s operation you’ll realize his ritual traces to Africa and very recent. Even Bill Gates ritual traces back to South Africa. His hooligans/investors must be an African white supremacy crowd.

>>10495212
The act of performing elimination doesn't have a geometric meaning. It is the same as using substitution to solve for unknowns.

The result that you get from elimination can be interpreted in two ways: it is the point of intersection of a system of planes (a point in n dimensional space that is located on each of the planes in the group) and it is also a linear combination of the columns of the matrix. The x_1, x_2...x_n values of the vector that solves the system are the scalar multiples by which you are multiplying each column of the matrix to get the right hand side. So when you arr given a coefficient matrix and a constant matrix and you solve the system, you consider the constant matrix as a point in R^n you want to get to and you are asking yourself "what linear combination of the columns of the coefficient matrix can get me to this coordinate?"

>>10495224
kek

>>10495212
1/9th, this 9th. Matterns.

>>10496506
Akhmed, we saw your wire tap already. Say your prayers to Allah, rat!

>>10495288
dont respond to the namefag. fuck off back to pleddit you basedboy bugman

>>10495212
for some reason I thought this was about Jordan blocks and shit
God i failed that class so hard. fuck jordan blocks and fuck jordan normal forms

>>10495225
producing that 3by3's inverse

>>10495224
Good one, anon.

>>10495224
haHA!

>>10496587
>The act of performing elimination doesn't have a geometric meaning. It is the same as using substitution to solve for unknowns.
implying substitution doesn't have geometric meaning