Understanding Linear Algebra: Dependent vs. Independent Vectors Explained

[dervast]

Hi i am new to linear algebra and i am not sure how i can translate some terms so i need some help with that
when we have vectorus u1,u2,.. un
and is k1*u1+k2*u2+...un*kn=0 then we say that these vectors are linear dependant or something like that
and if
k1*u1+k2*u2+...un*kn=0 and k1=0 and k2=0 and so on these vectores are linear independantly.
Do u know if my translation is correct?

 

[Office_Shredder]

Posted in the wrong place, but oh well.

We say $$u_1...u_n$$ are linearly independent if $$\sum{k_iu_i}=0$$ implies that all the k's are zero. They're linearly dependent if there are scalar k's such that not all of them are zero, and the above holds

 

[dervast]

And what is the physical meaning of linearly dependence and independence? What do u understand when y hear someone saying that something is linearly independent or dependent?

 

[Office_Shredder]

A set of vectors are linearly independent if, for n linearly independent vectors, you can describe n dimensions of space. So basically, it means that each vector you add describes a new dimension of direction. So the first vector points in a line, the second one lies in a plane with the first, the third lies in a volume with the first two, etc. If the vectors were linearly independent, then perhaps the first lies in a line, the second lies in a plane, and then the third also lies in that plane. So you don't get one dimension/vector

 

[dervast]

Thx a lot for the answers.but have u ever heard of any scientist to be using linear independability in a different fashion that the one u have just described?