Note that when you open up the Mathematica page, it starts with an error message. You may ignore that error messsage; simply hit the Graph button, and you will see the house.
Please modify the instructions as follows:
Also find the linear transformation that reflects the house about the y-axis.
Try to pick linear transformations with the range and nullspace you want. (Hint: If you pick a matrix at random, then almost certainly its range will be all of R^2 and its nullspace will consist of just the zero vector. So you'll have to have a plan to get a different range and nullspace. What's true about a matrix if its nullspace is 1-dimensional? What's true about a matrix if its nullspace is 2-dimensional? What happens to the range in each of these cases? Does there seem to be a relation between the dimension of the range and the dimension of the nullspace?)
Try to find relations between the range or nullspace, and the effect of the linear transformation on the house. Can you explain any of these relations? This is your main goal for this part (Step 4) of the investigation.