Question

wat do they mean by linear combinatin

Answer 1

A linear combination of vectors is basically the sums of any possible scalar multiples of those vectors. So, let's say for example you have the vectors (0,1) and (1,0). Then, a linear combination of those two vectors would be a(0,1)+b(1,0) for any a,b in the scalar field you're working in. You can see that in this example, the linear combinations can be any vector. For example, to make the vector (5,7) you would set a=7 and b=5.

Answer 2

ok wat do they mean by this
if a set of vectors {ai} is linearly dependent,then one of the vector is a linear combination of the others

Answer 3

That's basically just what it means for vectors to be linearly dependent. It means that one vector is a linear combination of the other vectors. Here's an example. Let's say we have a set of vectors: {(1,0), (0,1), (1,1)}. This set of vectors is linearly dependent, because we can write any of the vectors as a linear combination of the other ones. For example, (1,1)=(1,0)+(0,1).