here if i open the matrices and all i get 2 solutions but the detereminant of P is 0 so shouldnt it be infinite solutions???
#Matrices Determinants clash
uneven ingot
cinder moth
uneven ingot
@celest umbra need i quickhelp ;-;
celest umbra
Basis of null space of P. Wah
First check detP
They're basically asking no.of solutions to three homogeneous linear equations
detP = 0 implies infinite.
detP ≠ 0 means no solutions.
uneven ingot
yes but detP = 0
but also
theres only 2 solutions
so whats going on here
i solved it all
celest umbra
Forget the x²+y²+z² thing because you can scale down by some factor to get unit vectors
uneven ingot
just this smol thingy popped up
uneven ingot
Forget the x²+y²+z² thing because you can scale down by some factor to get unit ...
aayein
lavish river
Forget the x²+y²+z² thing because you can scale down by some factor to get unit ...
If the solutions for the linear equation turn out to be a plane or a line, this condition forces to reduce solutions.
Like the sphere of the above may cause solutions to be zero or 1 or smth
uneven ingot
If the solutions for the linear equation turn out to be a plane or a line, this ...
wait why does that happen
in the solution manual this is only what theyve done they frst said its infinite and then took lamda or smthing then said only 2
uneven ingot
Check rank of P then
ab ye kya hai
lavish river
Check rank of P then
But we gotta provide a "jee-ish" solution here 😭
uneven ingot
guys please this is mains level question no need to apply Grad math here
celest umbra
But we gotta provide a "jee-ish" solution here 😭
I'm in LA mode
uneven ingot
Like the sphere of the above may cause solutions to be zero or 1 or smth
what
what does that even mean
lavish river
what
I was just trying to highlight the x^2+y^2+z^2=1 thingy is in fact, very important to the question.
uneven ingot
I was just trying to highlight the x^2+y^2+z^2=1 thingy is in fact, very importa...
yes it is
usse answer to aaya
but like
lavish river
Wait Imma be back in a few...
uneven ingot
if detP = 0 then there should be infinte solutions of x y z
but theres infact only 2
how come so
it makes no sense its not like 2 of them are factors of each other either (x+y=0 and 2x+2y=0 wala i mean this is not there either)
lavish river
if detP = 0 then there should be infinte solutions of x y z
but theres infact on...
Okay...are you familiar with 3-d graphs?
Like have you played around in desmos 3d or smth?
uneven ingot
nopes
not introduced to 3D
distance formula wagera aata hai
11th ke sir ne kaha tha vectors 3D 12th me ek saath karwaenge
lavish river
Achcha but you know a linear equation in 2 variables gives a line when plotted right?
uneven ingot
Achcha but you know a linear equation in 2 variables gives a line when plotted r...
yea
lavish river
And what is analogous with a line in 3d?
uneven ingot
ik that 2 planes ka intersection can give point or line
uneven ingot
and thats a question as well how come if we consider these 3 planes to be intersecting we have not infinite not 1 but instead 2 solutions???
feels illegal
uneven ingot
So basically a linear equation in 3 when plotted gives a plane
yea
lavish river
and thats a question as well how come if we consider these 3 planes to be inters...
Jabh 2 planes are either superimposing, so the solution is a plane
Or when all 3 intersect to give a line
uneven ingot
Jabh 2 planes are either superimposing, so the solution is a plane
that would be infinte as well na
lavish river
In both cases solution is infinite
uneven ingot
haa
lavish river
and thats a question as well how come if we consider these 3 planes to be inters...
But we are also given the condition x^2+y^2+z^2=1
Which seems like a circle
So it is its analogue or a sphere
uneven ingot
But we are also given the condition x^2+y^2+z^2=1
OHHH
lavish river
still how 2
The solution (of linear eq.) must be coming out to a line and that line must be cutting the sphere two times na
uneven ingot
OH
I SEE I SEE
iska
3D
kaise bana sakta hu
in desmos
just for fun
samajh gaya ye to
lavish river
Desmos 3d is a thing
uneven ingot
bana sakta hu?
lavish river
bana sakta hu?
Yep.
uneven ingot
Desmos 3d is a thing
ok help me out a little here
lavish river
ok help me out a little here
Go to www.desmos.com and choose 3d calculator.
No embed perms here ig :/
celest umbra
uneven ingot
OH OKOK
can i have the uhhhhh 3 planes show their solution line
my PC is cooked bro it cant run this shi
lavish river
can i have the uhhhhh 3 planes show their solution line
It can't isolate the line but you can adjust your view so as to look at them intersect at a line
(Also I was gonna warn about the ram usage but...experimental learning is the best lmao)
uneven ingot
It can't isolate the line but you can adjust your view so as to look at them int...
areyyy okok
uneven ingot
(Also I was gonna warn about the ram usage but...experimental learning is the be...
damn fr
ok yall
thanks
+solved @lavish river