I'm sure you'll get responses from those with more expertise, but I wanted to point out a few things first. I haven't actually watched the intro to linear algebra video (doesn't seem to want to load for me right now), so some comments might be off base.
Be very careful with any Mathematica function that has "Form" in the name: MatricForm, TableForm, etc. You should think of these as special display-only functions. The basically wrap what you give them in a special "box" that causes the front end to apply special display rules. That special "box" will usually interfere with "normal" operations you might want to perform on your data. As soon as you apply MatrixForm, you no longer have a nice, simple matrix. You have a matrix hidden inside a "box", and that "box" doesn't understand arithmetic.
So, for example, for your vector v1, when you did this,
v1= {1,2,3} // MatrixForm
what you actually did was assign a special "box" to the variable v1. Inside that "box" is your vector, but anything you do directly to v1 will likely not be what you want. If you want to see v1 in matrix form, do the assignment first and then the display, like this:
v1= {1,2,3}; v1 // MatrixForm
Not sure how familiar you are with Mathematica, so I'll just note that you can put things on different lines or in different cells. Also, //
is just a pretty way to apply a head to an expression, so you could do
v1= {1,2,3};
MatrixForm[v1]