# Why is determinant 0 when vectors are linearly dependent?

### Why is determinant 0 when vectors are linearly dependent?

Why if the determinant of a set of vectors is zero these are linearly dependent?

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### Re: Why is determinant 0 when vectors are linearly dependent

Determinants:
https://www.math10.com/en/algebra/matri ... inant.html

Matrices & vectors: https://www.math10.com/en/university-ma ... ctors.html

You can try with this simple determinant:

1 2
5 10

1*10 - 2*5

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### Re: Why is determinant 0 when vectors are linearly dependent

Here are matrix calculators with steps:

https://www.math10.com/scripts/matrices ... ators.html

Math Tutor