@PaulTaylor Indeed that was my point. Here is my gmail: asghari.amir. Happy to hear from you and your friend.

@ZevChonoles Unfortunately, the paper is not available online. I have a scanned copy of the paper and I have just sent it to you. Please let me know if you have received it. Just in case, anybody else needs the paper, gmail me at asghari.amir

Indeed, my intention was to ask for "some insight into how professional mathematicians think about linear algebra". But, if I had asked that directly, the question was at danger of being "subjective and argumentative", and of course at danger of getting close. Thank you for reading between the lines

@GerryMyerson The reference of the course is Linear Algebra and Its Applications by Gilbert Strang. I didn't mention it earlier to avoid biasing the answer toward a certain idea.

Dear Vahid, many thanks for your answer. I am sure it doesn't matter that much, but since your answer was essentially the same as Todd's, I accepted his answer. He was first :)

Dear Mark. Many thanks for your answer. I "accepted" Todd's since as a "general" reader I learned more from that.

@BenjaminSteinberg if I do so, do they all get the reputation they deserve?

@BenjaminSteinberg And I wonder which one I shall "accept"! :)

The question you linked, and its answers, indeed also included both examples and counterexamples to some of my attempts to solve the problems. Thanks.

@StefanKohl At the first glance, I didn't get the point of Todd's answer. But, then I worked on the details, and I got it. Yet, I thank you for the details you added