II Find a least squars solution of \( A x_{i}=b \) for: \[ A=\left[\begin{array}{llll} 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 \end{array}\right] \quad b=\left[\begin{array}{c} -3 \\ -1 \\ 0 \\ 2 \\ 5 \\ 1 \end{array}\right] \]

Step 1 ：\(A^T A = \left[\begin{array}{cccc} 6 & 2 & 2 & 2 \\ 2 & 2 & 0 & 0 \\ 2 & 0 & 2 & 0 \\ 2 & 0 & 0 & 2 \end{array}\right]\)

Step 2 ：\(A^T b = \left[\begin{array}{c} 4 \\ -4 \\ 2 \\ 6 \end{array}\right]\)

Step 3 ：\(x_i = (A^T A)^{-1}(A^T b) = \left[\begin{array}{c} \frac{-3}{2} \\ \frac{5}{2} \\ 1 \\ \frac{7}{2} \end{array}\right]\)