We consider the mapping \( \varphi:\mathbb{R}^2 \to \mathbb{R}^2 \) given by \( A\in\mathbb{R}^{2x2} \). \(\varphi(\mathbf{v})= Av = v_1 \mathbf{a}_1+v_2 \mathbf{a}_2 = v_1 \varphi(e_1)+ v_2 \varphi(e_2)\)
	\(V= \mathbb{R}^2\)	\(\operatorname{range}(A)\subset \mathbb{R}^2 \)