(3). Let $T: \mathbb{R}^n \to \mathbb{R}^m$ be a linear transformation and A be its standard matrix, that is, $T \vec{x} = A \vec{x}$ for each $\vec{x} \in \mathbb{R}^n$. Please show that the range of T is just the column space of A. (10%)
(3). Let $T: \mathbb{R}^n \to \mathbb{R}^m$ be a linear transformation and A be its standard matrix, that is, $T \vec{x} = A \vec{x}$ for each $\vec{x} \in \mathbb{R}^n$. Please show that the range of T is just the column space of A. (10%)