Bases

## Description

We can use Sage to find the span and a basis of a vector space. If we simply print a vector space, we the basis is part of the information given. We can also use the basis method, which gives a list containing the basis vectors. For example, consider the span $W$ of $\mathbf v_1 = (1, 2, 3)$, $\mathbf v_2 = (4, 5, 6)$, and $\mathbf v_3 = (7, 8, 9)$ over $\mathbb Q^3$.

## Sage Cell

#### Code

V = QQ^3
v1 = vector(QQ, [1, 2, 3])
v2 = vector(QQ, [4, 5, 6])
v3 = vector(QQ, [ 7, 8, 9])
W = V.span([v1, v2, v3])
print(W)
W.basis()


none

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