I have a situation where I have two matrices, A and B. I am trying to solve for the detriment of B given certain information. I am have gotten to the following equation using properties of detriments:
det(B)*det(A) + det(B) = 10
I was given the matrix A which was just an upper triangular matrix, thus I computed the determent by taking the product of the main diagonal, this equates to 24. It is assumed that B is the same size as A.
det(B)*24 + det(B) = 10
My question is, am I allowed to factor out the det(B) here in order to isolate it and solve what the determinant would be, is this a mathematically sound thing to do?
det(B)(24 + 1) = 10
Thanks in advance.