A linear transformation $T\colon\mathbb{R}^3\to\mathbb{R}^2$ whose matrix is $\left(\begin{array}{ccc} 1 & 3 & 3\\ 2 & 6 & -3.5+k \end{array}\right)$ is onto if and only if $k\neq$__________
I'm a little confused by the notation here, so is the matrix given here supposed to be the matrix $A$ such that $XA \Rightarrow Y$? And what does the $\mathbb{R}^3$ and $\mathbb{R}^2$ notation mean? Does that mean a $3\times 3$ matrix and a $2\times 2$ matrix respectively?