MATH 21B Midterm: MATH 21B Harvard 21b Fall 07first Midterm Practice2
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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 un-staple the packet, please write neatly. Answers which are illegible for 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 needed. If a2 is invertible, then a is invertible. If a is invertible, then a3 is invertible. If a is a 3 3 matrix which is a rotation around a line inr3 then the columns of a form a basis ofr3. There is a matrix a and a vector ~b such that a~x = ~b has no solution and ker(a) = {~0}. The rank of a diagonal matrix a equals the number of non-zero entries in.
