I am given that $A$ is a $12\times 15$ matrix and the equation $Ax = b$ has a solution for every $b \epsilon \mathbb{R}^{12}$. What are the dimensions of the domain, the range and the kernel of $A$
I know that $Ax = b$ maps vectors from $\mathbb{R}^{15}$ to $\mathbb{R}^{12}$. Does this get me anything?
Secondly, do I know if the set of column vectors in $A$ is linearly independent and does this get me anywhere?