Least Squares Through Gram-Schmidt

A two-feature linear model is fitted to three data points. The design matrix and the target vector are

$A = \begin{bmatrix} 1 & 5 \\ 2 & 4 \\ 2 & -2 \end{bmatrix}, \qquad \mathbf{b} = \begin{bmatrix} 9 \\ 6 \\ 3 \end{bmatrix}$

$\mathbf{b}$ does not lie in the column space of $A$, so $A\mathbf{x} = \mathbf{b}$ has no exact solution.

Build $A = QR$ by Gram-Schmidt (first column normalized, second column's overlap projected out then normalized), and use the standard fact that the least-squares solution $\hat{\mathbf{x}}$ — the one minimizing $\|A\mathbf{x} - \mathbf{b}\|$ — satisfies

$R\hat{\mathbf{x}} = Q^{\mathsf{T}}\mathbf{b}$

What is $\hat{\mathbf{x}}$?