## Description

We can test a set of vectors for linear independence using the `.linear_dependence` mehtod. This method returns a vector containing the coefficients of a linear combination of the vectors in the given set that generates the zero vector, or an empty list if the only linear combination that generates the zero vector is the trivial linear combination (meaning the set of vectors is linearly independent). If the boolean statement at the end of the cell returns True, the set is linearly independent. If it returns false, the set is not.

## Sage Cell

#### Code

```
V = QQ^3
v1 = vector(QQ, [2, 3, 5])
v2 = vector(QQ, [7, 11, 13])
v3 = vector(QQ, [17, 19, 23])
V.linear_dependence([v1, v2, v3]) == []
```

## Options

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Date: 02 Jun 2020 15:44

Submitted by: Zane Corbiere