/sci/ - Science & Math

[Anonymous No.2121776]

Hey sci, head's full of fuck from pre calculus. Just what the hell are determinants for? How does it work, and what's its relevance to solving equations?

pic unrelated

[Anonymous No.2121789]

If det(A)=0, Ax=b has no (or infinitely many) solutions.
A vector cross product has a mnemonic that involves a determinant.
The Wronskian and Green's functions are determinants.

All I can recall for now.

[dolan !Uq56cE.45s No.2121786]

They're just stuff mathematicians created to look more intelligent. (the less people understand = the more they feel special) Don't pay attention to determinants.

[Anonymous No.2121793]

well you can check Cramer (or Kramer?) method
help to solve matrix equations for sure

[Anonymous No.2121802]

>>2121786
this.
I feel the same way about the majority of linear algebra as well.

[Anonymous No.2121805]

also if you want to invert a matrix you can use
A^-1 =A'/det(A)
where A' is the transpose matrix
if my memory still works

[Anonymous No.2121811]

OP here, is this used to solve equations with two or more variables?

for example:
y=3x-1
y=2x+3

I know you can evaluate this by elimination, but can you use determinants here? Or matrices (or wtf are those?)

[Anonymous No.2121822]

>>2121811
yep here you can use Kramer (Cramer?) method, but for a 2*2 dimension it's not that relevant

[Anonymous No.2121827]

>>2121811
Sure you don't mean descriminant? They would teach matricies before they taught the determinant.

[Anonymous No.2121843]

>>2121827
no, i'm pretty sure it's determinants. Weird, my professor just started blabbering about these fuck I haven't really encountered before and he started jamming it to our head. So I have to study this on my own.

>>2121822
oh so it really is used to evaluate equations' variables, like of by comparing them?

[Anonymous No.2121847]

Down with determinants!

They are pretty useless and all of Maths can be done without them. They are the wrong way of doing linear algebra.

[Anonymous No.2121872]

>>2121847
Yeah, I think I've encountered a problem in our lecture that the professor used another solution to evaluate equations, it was like simple algebra with all those expansions. Why the hell did they even bother using determinants? WTH.

[Anonymous No.2121881]

>>2121843
Well just with your example (hoping you know a little bit about matrix )... you have
3x-y=1
2x-y=-3
that you can write A*X=B with matrices
A= 3 -1 X= x B= 1
2 -1 y -3
then you can create two others matrices by replacing the columns in A by the vector B so lets call them C and D
C= 1 -1 D= 3 1
-3 -1 2 -3
And then you just find
x=det(C)/det(A)
y=det(D)/det(A)

For a 2*2 matrice the determinant is quite simple

M= a b
c d

gives det(M) = ad-bc

(hope there aren't too many mistakes here...)

[Anonymous No.2121883]

>>2121872
>>2121843
http://en.wikipedia.org/wiki/Matrix_(mathematics)


If the determinant is 0, that matrix has no inverse matrix. The determinant can also be used to find the inverse of a matrix.

Since matrices can be used to solve a system of equations, The determinant will also tell you if there are no solutions.

[Anonymous No.2121886]

ahhh crap, matrices are completely fucked up.. dont know if youre gonna understand ...

[Anonymous No.2121918]

Matrices defined:
"Matrices" is the plural of "matrix." The above system of equations in three variables is represented by this matrix equation (a 3x3 matrix times a one dimensional matrix (vector) equals a one dimensional matrix)

the equation:
x-2y+ z=-1
2x+ y-3z=3
3x+3y-2z=10

so that 3x3 matrix is actually the variables and its coefficients? And that one dimensional matrix are the constants on the other side?

[Anonymous No.2121939]

>>2121918
that may help you

[Anonymous No.2121960]

the determinant tells you many things ,but the most basic (and what gave it its name) is that it can tell you wether a system of equations have solutions or not.
(are they determined or do they have a free variable)

[Anonymous No.2121964]

Thanks guys, I think I kinda understand matrices now (but manipulating the numbers were kinda hard). Now I'm only down with determinants.

Anyways, this sounds dumb but how come we can actually solve for variables when there are two or more equations but cannot with only one equation?

[Anonymous No.2122000]

>>2121964
you need as many eq. as you have variables.

if you have x+y = 2
it can be x=2, y=0 or x=1,y=1 and so on.

but if we have the additional eq that 2x= -4
we can solve for x and y, and som get that
x=-2 , y= 4

[Anonymous No.2122008]

/r/ing dolphin vagina

Fried my old drive, so I don't have the pic anymore...

[Anonymous No.2122010]

well, in both case ( one or several equations) you will have some problems if it's not linear for instance (like variables to the power of something or derivative)

[Anonymous No.2122025]

>>2121793

It's Cramer, though I thought of Kramer when I learned it last week

[Anonymous No.2122033]

>>2122000
And to continue with that you can see each equation as a 'constraint' and each variable is a degree of freedom
so if you have more equations than variables you could have
x=3
x=4
you cant solve it
same number of equations and variables
x+y=2
x=3
one and only one solution

more variables
x+y=3, infinite number of solutions

Here it's just linear system, if it's non linear it's ... different