題組內容

2 Let $A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ and $\mathbf{b} = \begin{bmatrix} 1 \\ -1 \\ 5 \end{bmatrix}$.

b. (6) Let \( \mathbf{b}_A \) be the projection of \( \mathbf{b} \) onto the column space of \( A \). Find solution \( \mathbf{s} \) to \( A\mathbf{x} = \mathbf{b}_A \) such that \( \| \mathbf{s} \| \leq \| \mathbf{u} \| \) for all other solutions \( \mathbf{u} \).