Question

@ganeshie8 @kainui @openstudy quick question

Answer 1

I can take it too, right?

Answer 2

Is it about mathematics?

Answer 3

How can I tell a set of vectors is linear independent without having to calculate it, so I'm working on some eigenvalues and eigenvector stuff. It requires linear independent eigenvectors for the matrix. So when I did get these vectors I checked with wolframalpha and it did confirm they were linear independent.

So basically, I'm asking how can I figure out the eigenvectors are linear independent through inspection, I'm sort of thinking it could be because I've been getting free variables, could that be a hint?

Answer 4

@inkyvoyd

Answer 5

I teach inky though

Answer 6

idk but that asian might

Answer 7

oh crepe

Answer 8

hehe

Answer 9

He might know though, he's a smartie

Answer 10

Oh wait maybe if you find all the vectors and then see whether or not it can be represented by a linear combination of them, which will tell me whether it's linear dep or indep mhm

Answer 11

you could use determinants for this problem.
they make life easier.

Answer 12

Haha yeah that could work, actually you use that with differential equations whether to check their linear dependence, wronskian, you probably know of it

Answer 13

I want to be able to look at it and say yup that's lin indep!

Answer 14

what no... I'm not familiar with DE yet.
but determinants are so fun though. like they literally are zero iff there's some row or column that can expressed as a linear combination of other rows or columns respectively. so that's a neat idea.

Answer 15

What is the particular problem?

Answer 16

Oh it was a general question but the problem was