Matrices Determinants clash
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???
46 Replies
@Apu
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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.
yes but detP = 0
but also
theres only 2 solutions
so whats going on here
i solved it all
Forget the x²+y²+z² thing because you can scale down by some factor to get unit vectors
just this smol thingy popped up
aayein
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
I see
Check rank of P then
That'll help
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
ab ye kya hai
But we gotta provide a "jee-ish" solution here 😭
guys please this is mains level question no need to apply Grad math here
I'm in LA mode
infact its a Mains PYQ
please
have mercy on me
what
what does that even mean
I was just trying to highlight the x^2+y^2+z^2=1 thingy is in fact, very important to the question.
yes it is
usse answer to aaya
but like
Wait Imma be back in a few...
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)
Okay...are you familiar with 3-d graphs?
Like have you played around in desmos 3d or smth?
nopes
not introduced to 3D
distance formula wagera aata hai
11th ke sir ne kaha tha vectors 3D 12th me ek saath karwaenge
Achcha but you know a linear equation in 2 variables gives a line when plotted right?
yea
And what is analogous with a line in 3d?
ik that 2 planes ka intersection can give point or line
A plane
So basically a linear equation in 3 when plotted gives a plane
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
yea
Jabh 2 planes are either superimposing, so the solution is a plane
Or when all 3 intersect to give a line
that would be infinte as well na
In both cases solution is infinite
haa
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
OHHH
OHOHOOOOOO I SEE
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
OH
I SEE I SEE
iska
3D
kaise bana sakta hu
in desmos
just for fun
samajh gaya ye to
Desmos 3d is a thing
bana sakta hu?
Yep.
ok help me out a little here
Go to www.desmos.com and choose 3d calculator.
No embed perms here ig :/
desmos.com/3d
OH OKOK
can i have the uhhhhh 3 planes show their solution line
my PC is cooked bro it cant run this shi
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)
areyyy okok
damn fr
ok yall
thanks
+solved @SirLancelotDuLac
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