# 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