題組內容

6. Give the following system $\mathbf{Bx} = \mathbf{b}$ where $ \mathbf{B} = \begin{bmatrix} 1 & 1 \\ 2 & -3 \\ 0 & 0 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix}. $

(a)(10%) Find the least squares solution \( \hat{\mathbf{x}} \) for the system \( \mathbf{B}\mathbf{x} = \mathbf{b} \).