題組內容

5 Let $A = \left[ \begin{array}{cccc} 1 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 \end{array} \right]^\top \in M_{4 \times 2}(\mathbb{R})$ and $b = [1, 1, 0, 0]^\top \in \mathbb{R}^4$.



a. (10) Find \( \min{x\in S}\| Ax\| 2 \) and \( \max{x\in S}\| Ax\| 2 \) , where \( S = \{x\in \mathbb{R}^2\mid \| x\| _2 = 1\} \)