18.06  Linear Algebra

Hi 18.06,

As a reminder, the exam will cover everything we've covered in lecture (see syllabus for a refresher). There will be no additional emphasis on the material past the third exam, but you are responsible for everything, including linear transformations and anything else that came afterwards.

Best,
-Yan

Hi 18.06,

Course evaluations are due tomorrow. Please remember to enter them.

Good luck studying,
-Yan

Hi all,
  There was some confusion about the very first problem --- and it's all my fault.  A matrix is Markov if column sums add to 1 and the entries are non-negative.  There is a notion of positive Markov matrices that guarantee only one steady state.
  Anyway the correct answer was true to the first problem.  In many cases we accepted both answers, and sometimes subtracted one.
  Here's our proposed fix.
1.  Nobody will lose points already awarded, even if you got your test back.
2. We will give full credit to any answer that has no explanation or an explanation that is consistent with thinking
    that Markov means Markov or positifve Markov.  There were explanations that indicated lack of any understanding
   -- those will probably remain graded as they are.  (OK to say Markov means non-negative, or Markov means
         positive, not okay to say TRUE:because Markov matrices have positive entries when there was a 0,
    and not okay to say TRUE because the matrix is diagonalizable.)
3.  Tests not returned will be regraded and a new score may appear
4. Tests returned can be brought back to me in class tomorrow (Wednesday), this Friday, next Monday
      or to your TA's on Tuesday.  Tuesday next week is the final day.  Also ok to  put in the plastic bin outside
       my office in 2-343 if more convenient.  

Sorry for any confusion --- but now none of us will forget the official definition of a markov matrix.

Sincerely
Alan Edelman

Some information from the Professor:

8.1: will probably not be on the exams, but it's good material to know and you are certainly responsible for related skills such as recognizing positive definite and pos semidefinite matrices.

8.3: we only really covered up to p434 including the perron frobenius theorem. Don't worry too much about the remaining (Population Growth and the Consumption Matrix).

6.3: we really didn't cover 314-318 figuring this is also covered in 18.03 and elsewhere. Again, it is good to know and may give you intuition, but you won't be responsible for that material directly.

Good luck,
-Yan