Math 1B031st Sample Test #2Name:___________________________________________(Last Name) (First Name)Student Number:Tutorial Number:_________________________________________This test consists of 20 multiple choice questions worth 1 mark each (no part marks), and 1question worth 1 mark (no part marks) on proper computer card filling. All questions must beanswered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted forwrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that yourcopy of the test is complete. Bring any discrepancy to the attention of the invigilator.Calculators are NOT allowed.1.Determine which of the following matrices is a regular stochastic matrix, and then find thesteady-state vector for the associated Markov Chain.E œßF œßG œÞ!""!!""&%&#$""$#"#(a)(b)(c)(d)(e)#$$&""#"$$%&#%$""%#%2.After exposure to certain live pathogens, the body develops long-term immunity. Theevolution over time of the associated disease can be modeled as a dynamical system whosestate vector at time consists of the number of people who have not been exposed and are>therefore susceptible, the number who are currently sick with the disease, and the numberwho have recovered and are now immune. Suppose that the associated yearly$ ‚ $transition matrix has eigenvalues , and that the eigenvectors corresponding toEœ "ßß !-"#the first two eigenvalues are and , respectively. Thexx"#œ Ð'!ß #!ß $!Ñœ Ð'!ß $!ß *!Ñinitial state vector for the population is given byvxxx!"#$œ &!! #!! "!!where the third eigenvector is not given here. How many people will be sick with thex$disease 2 years later?(a)(b)(c)(d)(e)15450 27000 9700 4000)&!!3.Find the equation of the plane passing through , and .EÐ#ß "ß $Ñß FÐ$ß "ß &ÑGÐ"ß #ß $Ñ%B #D # œ !"!B %C D #" œ !'B $D $ œ !)B C $D ) œ !
MATH 1B03: Linear Algebra I
Instructor(s): N Anvari.
Prerequisites: One of Grade 12 Calculus and Vectors U, Grade 12 Geometry and Discrete U, MATH 1F03
Antirequisites: MATH 1ZC3
An introduction to linear algebra. This course discusses matrices and their properties, including determinants, eigenvectors/eigenvalues, diagonalization, and invertibility. Vector spaces are also defined and discussed more generally. This course reveals some of the ways in which matrices are used by computers to effectively manipulate data, and is relevant in many upper-year courses.
3 lectures and 1 tutorial per week (1 hour each).
Elementary Linear Algebra by Anton & Rorres
Casio fx991-MS/MS PLUS calculator
MATLAB- Computer Software
The course loosely was divided into three sections i) an introduction to matrices and their basic properties ii) further properties and iii) generalizing vector spaces. This third section acts as a basis for further studies in Linear Algebra. There is a test (midterm) after each of the first two sections and an exam at the end of the course.
EVAL 1: Tests 40% (20% each)
EVAL 2: Labs 10% (2% each)
EVAL 3: Assignments (2% each)
EVAL 4: Final Exam 40%
Other Useful Information
There is a large amount of theory within this course and is traditionally a student's first experience with a largely theory course. Understanding definitions and theory in conjuction with practice problems is important in doing well in the course.
Last modified on Thu Aug 6, 2015 at 8:37PM
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