determine whether the vector is in the image of A 
I am having a really hard time trying to understand what "the image of A" means and how to start such a question. 
I was thinking of creating a matrix with b1 as the augumented part of the matrix. 

The hint is in the text of your exercise. The image of $A$ is the abbreviation for the image of a linear map defined by the matrix $A$, i.e. $T:\Bbb R^3\to\Bbb R^3$ given by $T(x)=Ax$. To check whether a given vector $y$ lies in this image, you need to find the vector $x$ s.t. $y=Ax$. This leads to the system of linear equations.
