Random Vectors

## Description

We can produce random elements of a vector space with the .random_element() method. This is useful for generating elements of the span of several vectors. For example, if we consider the subspace of $\mathbf Q^3$ spanned by vectors $(2, 3, 5)$ and $(7, 11, 13)$, then we can use random_element to generate random vectors in the span.

## Sage Cell

#### Code

V = QQ^3
S = V.span([vector(QQ, [2, 3, 5]), vector(QQ, [7, 11, 13])])
vecs = [(i, S.random_element()) for i in range(10)]
vecs


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