Well, if you stand on really strong foundations, you can picture everything that happens in your minds eye. It’s algebra with a geometric twist. Simplest example I can think of now is intersections of planes as solution spaces, thats the picture you could imagine from a bunch of equations. Sorry I had it 4 years ago but at the time I could have written better about it. I used contemporary linear algebra, howard anton. Another simpler example is span, the total space of points that you can get by adding and scaling specific vectors that you have. Imagine an infinite plane created by the configurations of two vectors.