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10:05 PM
@Hippalectryon u here
 
@Karlo ye
 
if adjugaded amount is t_{ij}
why
 
x_{p1}t_{r1}+....x_{pn}t_{rn}=0 if
r and p are rows and they are diffrent
 
Once again, is that a question or a statement ?
 
10:09 PM
question
I forgot why sorry
if p=r it is equal to Det I know that
but if they are not
it means we have have 2 equal rows ?
 
I don't get your question.
 
If we pick a row in a matrix for e.g we can calculate the determinant by the adjugated amounts
and we calculate it by the formula above
if we pick the row p and the adjugated amounts of that row
but if we pick amounts of diffrent row
we get 0
 
We have that
$-2 \sqrt{2} < x < 2 \sqrt{2}$ : $5$ integers
$-2 \sqrt{2} < y < 2 \sqrt{2}$ : $5$ integers
$-2 < z < 2$ : $3$ integers

To find how many non-trivial points $(x, y, z)$ we multiply $5 \cdot 5 \cdot 3$ and substract $1$, which is the case $(0, 0, 0)$, or not??

Then the result is $74$, but in my notes I have that there are $72$ cases... How do we get this result??
 
@Karlo I still don't get your question :/ could you try to formulate it clearly, in one sentence ?
 
you know how to find the determinant by row and adjugated amounts right?
for example lets pick the first row
det=x_1.t_1+x_2.t_2........x_nt_n
but suppose u get the adjugated amounts of the second row
then the product is not det it is 0
 
10:17 PM
@Karlo The determinant of a row ?? Determinants are for $n\times n$ matrixes...
 
look if you have
3x3 matrix with entries
from 1 to 9
det = 1. Det 5 6 7 8 + (-2).det 1 3 7 9 ....
 
Can you write that in Latex ?
 
sure second
Say $t_{ij}$ is the matrix without i column and j row
it is known that determinant can be evaulated by the formula
x_1.det(t_{11})-x_2det(t_{12}).......x_n.det(t_{n1})
 
Can you put dollar signs around your latex please ? It's easier to render.
 
yes second
$Det(A)=x_1.det(t_{11})-x_2det(t_{21}).......x_n.det(t_{1n})$ where$ t_{1n}$ is the matrix without 1 row and n column.Now if you choose
the adjugated amounts of other matrix the result will be 0 why
 
10:29 PM
"Now if you choose
the adjugated amounts of other matrix" what do you mean ?
 
you pick the next row
and find it's amounts
and if you multiply them by the first row
u will get result 0
$0=x_1.det(t_{21})-x_2det(t_{22}).......x_n.det(t_{2n})$
 
Finally, someone is making @Hippa earn his keep.
 
@TedShifrin q_q
@Karlo I don't have a clue what you mean by "and find it's amounts".
Maybe @TedShifrin knows
 
find the determinant
without the following row and column that is adjugated amount
 
There's no determinant of a row
"you pick the next row
and find it's amounts"
 
10:35 PM
@Karlo: If you use the adjugates of a different row, then you are calculating the determinant of a matrix with two equal rows.
 
that is what I want to hear
thanks :P
 
SuperTed solves everything
 
Make sure you understand :P
 
oh and superted :D
 
glares @Hippa
 
10:36 PM
what is the connection between the rank of rows and columns
 
I just discussed this in my class yesterday, @Hippa :P
 
so i can prove they have equal rank
 
There are lots of different proofs, @Karlo. I don't know what you know and what you don't.
 
the easiest
cause I don't know how to connect them :?
 
Well, you can give a mapping from the row space (span of the rows) to the column space (span of the columns) which is 1-1 and onto.
 
10:40 PM
ok
@TedShifrin from which it follows that the result of polylinear antisymmetric function is a determinant of a matrix
 
I don't see how the two are related
 
hi @ted
 
hi @Ramanewb
 
@ted I'm not as tired as yesterday this evening...
 
if f(x1....xn) you place x1=R1
where R1 is the row of a matrix
it follows
and you set the basis to be the standart one
 
10:44 PM
@ted I am given $A\left(-8;3\right)$, $B\left(-6;-6\right)$, $C\left(-7;2\right)$.

I want to calculate the equation of the median from C.

If M is the point such that $\left(MC\right)$ is the median from C,

$MC : y=mx+p$

$m=\dfrac{\frac{y_a+y_b}{2}-y_c}{\frac{x_a+x_b}{2}-x_c}$, So

$m=\dfrac{\frac{y_a+y_b}{2}-y_c}{\frac{-8-6}{2}+7}$, So

$m=\dfrac{\frac{y_a+y_b}{2}-y_c}{0}$

And that's impossible ! Although, I now this equation exists... Where does it go wrong is what's just above ?
 
We did this all last night, @Ramnewb. Go review.
 
@ted last night we found that the equation can be written as x=k
 
We got farther than that.
 
@ted not really... I was too tired and had to go to sleep !
 
Well, scroll up and review the record.
 
10:46 PM
@ted the problem is that a correct solution is $-\frac{49}{2}-\frac{7}{2}x=0$
 
@Karlo: I still don't follow entirely. You're defining determinant in terms of columns and trying to prove you get the same answer for rows?
 
@ted how do you explain that ??
 
@Ramanewb: I tell you to simplify the arithmetic.
 
@ted I don't get what you mean when you say "smplify the arithmetic", sorry...
 
That equation can be made much more simple.
 
10:48 PM
what one ? @ted
@ted this one ? $-\frac{49}{2}-\frac{7}{2}x=0$
 
Indeed.
 
@ted do I have to put it like the model $x=k$ ?
 
@TedShifrin can you explain in other words why row rank is equal to column rank
 
I'm confused, @Karlo. Are you trying to prove that with determinant, or are you using that to prove something about determinant?
 
nono i figured the adjugated amounts
i just don't know why row ranks is equal to column rank
 
10:52 PM
I do not follow you.
 
you explained it
but i could not understand it
 
Again, I do not know what you know and what you do not know, so this is a failing of this site. Better for you to ask your own teacher, who knows what you know.
 
I have a solution including to prove that the rows are spaces
and from there it folllows
but I can't understand it
so if you know similar proof
 
You should take a basis $\{v_i\}$ for the row space and use it to define a basis $\{Av_i\}$ for the column space. If you prove that the latter is a basis, then they have the same dimension.
 
@ted what's the point of the carthesian form ? Why do they say $-\frac{49}{2}-\frac{7}{2}x=0$ and not just $x=-7$ ?
 
10:56 PM
Don't ask me, @Ramanewb.
 
@ted why ? don't you know ? or maybe you're not interested in that ?
 
Nope.
 
ok @ted nevermind... tks
 
There is no answer to why someone would say $3x=6$ is the equation instead of $x=2$. Presumably it's a computer that's been programmed and it hasn't reduced things.
 
@ted that may be right, ot's made by a computer
 
10:58 PM
And badly programmed so it doesn't reduce things.
 
@hippa do you have the answer ? Is there a utility of the carthesian form when we can write it simplier ?
 
@Ramanewbie The answer is go to bed
 
@ted maybe it's volunteeer, I don't know....
 
And it's Cartesian. Leave Carthage out of this.
 
smacks @Hippa ...
 
10:59 PM
@hippa oh I didn't see the time !
it's late again @hippa !
 
m'enfin, Descartes était français :P
 
@TedShifrin O_o_O
 
@ted sure he is !
 
Bonne nuit, @Ramanewb
Clearly your parents control neither of you brats, @Hippa.
 
@TedShifrin Hehe. I'm not at home.
 
11:00 PM
I knew that, @Hippa, but petit frère is.
 
good night everyone !
yes I am...
 
11:30 PM
someone herre?
 
I                            I
11:47 PM
yup
 
so when we try to make a matrix in echelon
sometimes we have infinitly many solutions
and we have to parametrize
and this depends on n-r (n length ot matrix by rows and r -zero rows)
why is that
 
I                            I
I can't help you, I'm in general new to 'harder' math
 
ok
 
I                            I
I'll look what echelon is
 
gauss elimination
 
11:50 PM
Has anyone got an example of a function $f(x)$ (other than the gamma function) that satisfies $f(x+1)=xf(x)$ and $f(1)=1$?
 
@user112495 $$f(x) = \Gamma(x)\cdot (1 + \sin (2\pi x))$$
 
@DanielFischer Thanks! Just out of interest, are there any (fairly simple) functions satisfying those properties that don't contain the gamma function?
 
I                            I
@Karlo I won't help you
 
@user112495 Don't know. I think the "fairly simple" implies a simple-ish modification of $\Gamma$, but maybe it doesn't.
 

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