MATH 21B Midterm: MATH 21B Harvard 21b Fall 07first Midterm Practice1 Solution
Document Summary
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. A linear system with 2 equations and 3 unknowns has either in nitely many or no solutions. Geometrically, this is an intersection of two planes. They are either the same plane or intersect in a line. If s is an invertible matrix which contains the vectors ~v1, , ~vn as columns, then ~v1, , ~vn is a basis of rn. This is an important property of a basis in rn.
