- #1
drosales
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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<i,j<n. Show that det(B)=(-1)ndet(A)
Hint: use the definition of determinant
I honestly have no idea how to go about this. I'm assuming it has something to do with elementary row operations and the sign of the determinant changing with each operation but am not quite sure how to get started. Any help would be great.
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<i,j<n. Show that det(B)=(-1)ndet(A)
Hint: use the definition of determinant
I honestly have no idea how to go about this. I'm assuming it has something to do with elementary row operations and the sign of the determinant changing with each operation but am not quite sure how to get started. Any help would be great.