Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 36

$T$ is a linear transformation from $R^5$ into $R^2$

Let $A$ be a $m\times n$ matrix. The function $T$, defined by $T(v)=Av$, is a linear transformation from $R^n$ into $R^m$. Here, since $A$ is $2\times 5$, implies $n=5,m=2$. So, $T$ is a linear transformation from $R^5$ into $R^2$