1.4.7 Matrix transformations

condition: Given: \( A=\left(\begin{array}{ccc}1 & 4 & 4 \\ 1 & 4 & 2 \\ -2 & 2 & -3 \\ 1 & -1 & 1\end{array}\right), b=\left(\begin{array}{c}-12 \\ -4 \\ 13 \\ 1\end{array}\right) \). Orthogonalize the columns of the matrix \( A \) and find a pseudo-solution of the system \( A x=b \).