Consider the following two models where $E(\boldsymbol{\varepsilon})=\mathbf{0}$ and $\operatorname{Var}(\boldsymbol{\varepsilon})=\sigma^{2} \mathbf{I}$ :

Model A: $\mathbf{y}=\mathbf{X}_{1} \boldsymbol{\beta}_{1}+\boldsymbol{\varepsilon}$

Model B: $\quad \mathbf{y}=\mathbf{X}_{1}^{\prime} \beta_{1}+\mathbf{X}_{2} \beta_{2}+\varepsilon$

Show that $\quad R_{\mathrm{A}}^{2} \leq R_{\mathrm{B}}^{2}$.