# MIDTERM SOLN - Faculty of Mathematics University of...

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Chapter 15 / Exercise 42
Finite Mathematics and Applied Calculus
Costenoble/Waner
Expert Verified
Faculty of MathematicsUniversity of WaterlooMath 235Midterm Examination - Fall 2014Time:4:30 - 6:20 pmDate:Nov 4th, 2014.Family Name:First Name:I.D. Number:Signature:Section 01J. Resch (1:30)Section 02J. Resch (10:30)Section 03S. Gindi (10:30)Section 04R. Seyyedali (11:30)Section 05B. Rooney (1:30)Section 06B. Rooney (10:30)Your answers must be stated in a clear and logical form andyou must show all of your steps in order to receive full marks.Instructions:1. Completetheinformationsectionabove, indicating your section by acheck mark in the appropriate box.2. Place your initials at the top cornerof each page in the space provided.3. Make sure you have all the pages andobserve the test is double-sided.4. Answer the questions in the spacesprovided,usingthelastpageforoverflow work and making indica-tions that work is to be continuedthere.5. No calculators are allowed.QuestionMarkValue119210311410522Front Page1Total73
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Chapter 15 / Exercise 42
Finite Mathematics and Applied Calculus
Costenoble/Waner
Expert Verified
Math 235 - Midterm ExamPage 2 of 11Initials:1. Answer the following questions(a) LetAMn×n(F). Define the Row(A) and the Col(A). What can we say about thedimension of the Row(A) and the Col(A)? [3]
(b) State the Rank-Nullity Theorem. [2]
(c) ConsiderL:VVwhere V is a vector space overF. Supposeβ={v1, . . . ,vn}isa basis for V. Define theβmatrix of L (typically denoted as [L]β). [1]
(d) Let W be a subspace of a finite-dimensional inner product space V overR. Definethe orthogonal complementW. What is the dim(W)? [2]