CHAPTER 02.12: VECTORS: What do you mean by linear combination
of vectors? In this segment, we’ll talk about what we mean by
a linear combination of vectors. SO let’s suppose somebody gives you m
vectors. A1, A2, all the way up to Am or “m” vectors of dimension “n”. SO the
dimension of each vector is “n” and the number of vectors which are given to
you are “m”; then is k1, k2, all the way up to km are “m” scalars, then if we
multiply – let’s suppose the first vector A1 by k1. Then we take another
vector A2 and multiple it by another scalar k2 and we keep on doing this. So
we take the mth vector and we multiply by km, then
that’s considered to be a linear combination of “m” vectors. So all you are doing here is that you are taking –
if somebody says “Hey, find a linear combination of “m” vectors which are of
dimension “n””, you take each vector multiplied by come scalar. Whatever
comes out to be the solution or the answer is your linear combination of “m”
vectors. And that’s the end of this segment. |