Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 34

$T$ is a linear transformation from $R^2$ into $R^3$.

Let $A$ be $m \times n$ matrix. The function $T$ defined by $T(v)=Av$ is a linear transformation from $R^n$ into $R^m$. Here, since $A$ is $3\times 2$, implies $n=2,m=3$. So, $T$ is a linear transformation from $R^2$ into $R^3$.