Let vec(v_1) = [( 2),(3)] and vec(v_1) = [( 4),(6)] what is the **span** of the vector space defined by vec(v_1) and vec(v_1)? Explain your answer in detail?
1 Answer
Explanation:
Typically we talk about the span of a set of vectors, rather than of an entire vector space. We will proceed, then, in examining the span of
The span of a set of vectors in a vector space is the set of all finite linear combinations of those vectors. That is, given a subset
(the set of any finite sum with each term being the product of a scalar and an element of
For simplicity, we will assume that our given vector space is over some subfield
= {lambda_1vecv_1+lambda_2vecv_2|lambda_1,lambda_2inF}
But note that
Then, as any linear combination of