Question

Can someone explain to me the difference between linearly dependent, linearly independent & basis?

Answer 1

Gladly :)
In a vector space, if we have a set of vectors v1, v2, v3...vn
then a linear combination of these vectors would take the form
a1v1 + a2v2 + a3v3 +... anvn for some scalars a1, a2, a3, ... an

Such a set of vectors is called linearly INDEPENDENT if the only linear combination of the vectors that would be equal to the zero is if all the scalars themselves are zero.

It's called linearly dependent if it's not linearly independent.

It's a basis if it's the maximal linearly independent set.
What that means is that the set is linearly independent, and if you add any other vector from the vector space, then the set becomes linearly dependent.

Answer 2

how about span?

Answer 3

that set of vectors is said to span the vector space if every vector in the vector space can be written as a linear combination of the set of vectors.

That gives us another way to view the basis:
A basis is a set of vectors which is linearly independent AND spans the vector space ;)

Answer 4

thank you...