I definitely covered the column space and row space in my undergrad LA class, long before I had ever heard of Strang.
An exceptional minority of people has the ability to learn linear algebra in its full abstract generality as their first treatment of the material, and come away with something resembling an understanding.
The rest of us dopey oafs must develop intuition carefully from specific concrete examples that extend gradually from algebra and geometry that we are familiar with already. Those of us in this sad deficient category must be led painstakingly over several weeks of course material to even the basic idea that a matrix is just a particular representation and special case of something called a linear transformation.
If you are one of the former type, you are blessed, but it's unfair to sneer at the latter, and it will only do your students a disservice.
An exceptional minority of people has the ability to learn linear algebra in its full abstract generality as their first treatment of the material, and come away with something resembling an understanding.
The rest of us dopey oafs must develop intuition carefully from specific concrete examples that extend gradually from algebra and geometry that we are familiar with already. Those of us in this sad deficient category must be led painstakingly over several weeks of course material to even the basic idea that a matrix is just a particular representation and special case of something called a linear transformation.
If you are one of the former type, you are blessed, but it's unfair to sneer at the latter, and it will only do your students a disservice.