Why is determinant 0 when vectors are linearly dependent?

[Guest]

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

[Math Tutor]

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

[Math Tutor]

Here are matrix calculators with steps:

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