Paul
Posts:
451
Registered:
7/12/10


Re: Linear Algebra Question
Posted:
Apr 15, 2014 3:50 AM


On Monday, April 14, 2014 3:00:09 PM UTC+1, dull...@sprynet.com wrote: > On Sun, 13 Apr 2014 20:56:00 0400, George Cornelius > > <gcornelius@charter.net> wrote: > > > > >On 04/13/2014 12:25 PM, dullrich@sprynet.com wrote: > > >> Just realized I've been lying to my students for years. > > >> > > >> Q. Say A is a 2x2 real matrix, b is in R^2 and b <> 0. > > >> Let S = {x in R^2 : Ax = b}. Is S closed under addition? > > > > > >Maybe you confused it with the set of x > > >such that A x = c x . > > > > > >True for all c, of course. > > > > No. See Goddard's reply for a hint, or Magidin's reply > > iif you want to see it all worked out. The definition > > of S is what I meant  it may or may not be closed > > under addition.
Are there pedagogical lessons to be learned from the fact that none of your students pointed this out?
Perhaps profs need to say things more often like "I do make mistakes sometimes, so check what I say before taking my word for everything. Also, I don't necessarily prove things in the best way possible, so, if you can find improvements, that's also good."
My impression (partly from the very fact that you support these democratic forums so actively) is that you are probably a less authoritarian figure than most profs, and probably do say this type of thing.
But maybe there's too much of a culture of uncritical trust in our teachers as authority figures. There certainly was when I was a student but that was a long time ago.
Paul Epstein

