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?
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
But note that
Then, as any linear combination of