Linear Mappings and Matrices

Consider the mapping \( T:\mathbb{R}^2 \to \mathbb{R}^2 \):
\(T(\mathbf{x})=A\mathbf{x}\)

 
\( V= \mathbb{R}^2 \)

\(\operatorname{range}(A)\subset W= \mathbb{R}^2 \)