題組內容

5 Let \( \mathbf{x},\mathbf{y}\in \mathbb{R}^n \) and \( A = I_{n} - \mathbf{x}\mathbf{y}^{T} \)

c. (5) Show that \( \operatorname{det}(A) = 1 - \mathbf{x}^T\mathbf{y} \).