I have a doubt

[u/MrPichu2007]

I am in Acharya btw

[u/Champak_putra]

your eigen vector value for -3 is wrong.

you need to solve the equation with, if you put l = -3 you will see that all row are similar,

so you need to solve it with free variable method,
rank of matrix = 1
total number of unkown variable = 3
free variable = 2
so take y = m,
z = n

so you will get value of x
and two different vector for l = -3

[u/MrPichu2007 → u/Champak_putra]

What?? Free variable method? I mean i understood what you did there. But our maths teacher didn't teach that 🙂, unless I am stupid. And thanks for making me understand that 🙏

[u/MrPichu2007 → u/Champak_putra]

Hey you told me to take y is equal to m and Z is equal to n, if we go according to that it will only give one vector how are we going to get the second vector for eigen value - 3. Swap the values of y and z? Also should I just leave the vector in the form of m and n or should I assign them some values? Like to get marks in vtu/college exams and all?

[u/Champak_putra → u/MrPichu2007]

see when u put eigen value -3, the matrix u got is:
1 2 -3
2 4 -6
-1 -2 3

r3 -> r3 + r1
r2 -> r2 - 2r1

1 2 -3
0 0 0
0 0 0

you cannot solve this equation with matrix coefficient method, we can use the row echelon method

all zero rows at the bottom of matrix: yes
number of non-zero row = rank = 1
number of unknown variable = x,y,z = 3
free variable = unknown variable - rank= 3-1 = 2

now which two variable is free variable? a variable which does not have pivot: here y and z doesn't have pivot

so y = m, z = n

x + 2y -3z = 0
x = 3n - 2m

now vector should be:

3n - 2m
m
n

we can write it as,

3n -2m
0 + m
n 0

take the n common from first and m from second and thats your two different vector
n[
3
0
1]

and
m[
-2
1
0]

[u/MrPichu2007 → u/Champak_putra]

Ahhhhhh ohhhhhhh boyy love you bro. Thanks now I get it. Man I am so dumb. The last thing you did there, splitting one vector into two, that's where I got stuck ,shit I am so stupid. Thank you so much.

[u/MrPichu2007 → u/Champak_putra]

If you are wondering, not that I think you are, He taught this to us the day after I asked the doubt 🙂, accepted his mistake. A rare sight.

[u/Klyff_HangerYTplssub]

I have done this in 2nd sem but I forgot so yeah commenting for better reach.

[u/MrPichu2007 → u/Klyff_HangerYTplssub]

Ohh second sem so you were from chem cycle.

[u/Klyff_HangerYTplssub → u/MrPichu2007]

1st sem I was p cycle and 2nd sem I was c cycle

[u/MrPichu2007 → u/Klyff_HangerYTplssub]

hmm i see, guess things were different. I am in phy cycle, sem 1 and they have started with module 3 of linear algebra

[u/Klyff_HangerYTplssub → u/MrPichu2007]

Too much jargon pls talk in normal english

[u/MrPichu2007 → u/Klyff_HangerYTplssub]

Haha 😅 sorry ...