Let AAA be an n×nn \times nn×n matrix. What is the value of det(I+xyT)\det(I + xy^T)det(I+xyT) where x,yx, yx,y are column vectors?
1+xTy1 + x^T y1+xTy
1+yTx1 + y^T x1+yTx
1+∥x∥∥y∥1 + \|x\| \|y\|1+∥x∥∥y∥
0