5. (30%，each 15%)

(a) Given $\mathbf{A} = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 0 \\ -1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. Find the Gram-Schmidt $QR$ decomposition of $A$, then use that decomposition to solve the least squares problem.

(15%)