18.06  Linear Algebra

To help you prepare for the exam, there will be additional office hours this weekend, as follows:

Saturday, 6-7 PM (Denis)
Sunday, 7-9 PM (Cheng - first hour, Eva - second hour)

The location on both days will be the 2-390 alcove.

Due to low popularity of the previous time slot, the office hours of Cheng Mao have changed to 19:30-20:30 on Thursdays in the common space of 2-333 or 332, effective today.

Due to the test, this week there won't be Nardin's office hours on Wednesday 09/21

We would like to remind to all students that, in addition to recitations and office hours, MIT offers two services for help with classes: Math Learning Center (Monday to Thursday, 3pm–5pm and 7:30pm–9:30pm in 4-159), organized by the math department, and Talented Scholar Resource Room, organized by the Office for Minority Education.

Since several people have emailed me asking about this, here is a further clarification.



In question (i) the vectors e_1,e_2,e_3,.. are the ones I described in my earlier announcement: e_i has the i-th coordinate equal to 1 and all the other coordinates equal to 0. They are often called the "standard basis vectors" for reasons that will be apparent soon.  The problem is asking you to write the standard basis vectors as a linear combination of the given vectors or, if it is not possible, to explain why. Here are some example  a') (1,1); (1,-1) SOLUTION: e_1 = 1/2 (1,1)+1/2 (1,-1); e_2 = 1/2 (1,1) - 1/2 (1,-1);  b') (1,1); (-1,-1) SOLUTION: It is impossible to write e_1 or e_2 as a linear combination of the given vectors, since all of the given vectors are multiple of (1,1) and so their span consists of multiples of (1,1), and e_1 and e_2 do not lie in it.