# Linear Algebra: Determinant

by drosales
Tags: algebra, determinant, linear
 P: 9 I'm having trouble with this problem on my homework Let n be a positive integer and A=[ai,j] A is n*n. Let B=[Bi,j] B is n*n be the matrix defined by bi,j=(-1)i+j+1 for 1
 PF Patron Sci Advisor Emeritus P: 8,837 A good start would be to write down the definition of the determinant. Specifically, what does the definition say that ##\det B## is? Did you mean ##b_{ij}=(-1)^{i+j+1}a_{ij}##?
 P: 9 Yes, that is what was meant. I didnt realize I didnt complete that
PF Patron
Emeritus
P: 8,837

## Linear Algebra: Determinant

So what does "det B" mean for an arbitrary n×n matrix?
 P: 9 My understanding is that det(B) is the sum of the cofactor expansions multiplied by minor matrices
 PF Patron Sci Advisor Emeritus P: 8,837 This is usually derived from a definition involving a sum over all permutations of {1,...,n}. I think that definition will be easier to work with.
 P: 9 Would you mind explaining it? I have it in my lecture notes but I have trouble following
 PF Patron Sci Advisor Emeritus P: 8,837 I think you have to be more specific about what's causing you trouble. I mean this definition: http://en.wikipedia.org/wiki/Determi...-by-n_matrices

 Related Discussions Introductory Physics Homework 4 Precalculus Mathematics Homework 12 Calculus & Beyond Homework 1 Calculus & Beyond Homework 3 Calculus & Beyond Homework 1