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added definition of 3x3 determinants (#23844)

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added additional info about 3x3 determinants and their meaning (geometrically) as well as the fact that they are also the volume of a parallelepiped.
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Jack Kang
2019-02-10 13:19:04 -05:00
committed by Randell Dawson
parent 766d217b94
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guide/english/mathematics/3-by-3-determinants/index.md
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title: 3 by 3 Determinants
---
## 3 by 3 Determinants
3x3 determinants are a value that can be calculated by the values in a matrix. It is also known as the scaling factor of the linear transformation that the matrix represents.
When a 3x3 matrix and its rows are comprised of three vectors, the determinant of this 3x3 matrix is the volume of the parallelepiped that is made up of these three vectors.
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Determinant_parallelepiped.svg/950px-Determinant_parallelepiped.svg.png" width="400">
## Calculation
### Method 1
Consider the following matrix, which we will call A: