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# What are matrices' determinants used for??

How are they helpful in the real world--or maybe just their plain uses...??

### 2 Answers

- 1 decade agoFavorite Answer
they are used to find the perpendicular vector to two given ones in 3 dimensional space.

they are used to check if a linear transformation is bijective, or not ( if det =0).

given a paralelepiped formed with 3 vectors, the determinant of the matrix determined by these vectors = volume of the paralelepiped. .

- Sean HLv 51 decade ago
I don't know if I can speak to the use of determinants in the "real world," but here some ways they are used in mathematics:

1) In Cramer's Rule to find the inverse of a matrix. I suppose inverting matrices is probably important in some real world applications...

2) Changing variables in integrals.

3) Calculating the volume of certain objects.

Well, that's all I can think of at the moment.