MATH 21B Midterm: MATH 21B Harvard 21b Spring 18Midterm 1
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Tth 11:30 alison miller: start by writing your name in the above box and check your section in the box to the left, try to answer each question on the same page as the question is asked. If needed, use the back or the next empty page for work. If you need additional paper, write your name on it: do not detach pages from this exam packet or unstaple the packet, please write neatly and except for problems 1-3, give details. Answers which are illegible to the grader can not be given credit: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. Problem 1) tf questions (20 points) no justi cations are needed. Any 88 77 matrix a has exactly 88 columns. If a system of equations ax = b has in nitely many solutions, then a has a non-trivial kernel.