# Let V be a 5 dimensional vector space

1. May 26, 2005

### laminatedevildoll

Let V be a 5 dimensional vector space, and let $$\Delta$$ be a determinant formon V. Given $$\Delta$$(b1, b2, b3, b4, b5)= -3

How do I find $$\Delta$$(b4, b3, b5, b1, b2)?

2. May 26, 2005

### mathwonk

use properties of determinnats, i.e. interchanging two rows changes the determinant by a minus sign. did you know this? if not, go back and review what properties determinants have.

or let me just tell you:

a determinant is an
1) alternating
2) multilinear
3) normalized

function of n variables, where n = dim(V).

normalized means that if there is some preferred basis, like e1,....,en, then det(e1,...,en) = 1.

more intrinsically, if it is only defined for endomorphisms, then det(Id) = 1.

Last edited: May 26, 2005