midterm1solutions

# midterm1solutions - Midterm 1, Math 33A, Fall 2007 October...

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Unformatted text preview: Midterm 1, Math 33A, Fall 2007 October 26, 2007 Name: Section (circle the one you regularly attend, as this is where the exam will be returned): 2A Jack Buttcane Tuesday 2B Jack Buttcane Thursday 2C Judah Jacobson Tuesday 2D Judah Jacobson Thursday Directions: Fill in your name and circle your section above. Do not turn the page until instructed to do so. You have 50 minutes to complete the exam. No outside materials are allowed; use only your brain and a writing instrument. There are 3 problems; each is worth 10 points total. Extra scratch paper is included. If your work on a problem appears on a different page, indicate clearly where it may be found. Show all the necessary steps involved in finding your solutions, unless otherwise instructed. In the interest of us not losing pages of your exam, please refrain from detaching pages from the exam. Good luck. Problem Score 1 2 3 Total 1 1. Indicate whether each statement is true or false; you need not show your work here. If the vectors ~v 1 ,~v 2 ,~v 3 are linearly independent, then the vectors ~v 1 ,~v 1 + ~v 2 ,~v 1 + ~v 2 + ~v 3 must be linearly independent as well. T F If A is a n by m matrix and the columns of A are linearly independent, then the dimension of image A must be m . T F If A and B are 2 by 2 matrices, A represents counterclockwise rotation by an angle about the origin, and B represents reflection across the x 1-axis, then BA must equal A- 1 B . T F If A is a matrix, then ker...
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## This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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midterm1solutions - Midterm 1, Math 33A, Fall 2007 October...

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