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 !
1B03/1ZC3 LINEAR ALGEBRA COURSE OUTLINE Instructor: Dr. Nima Anvari Email: [email protected]Oﬃce Hours: Tuesday and Thursdays 5:00-6:00 HH 407 Course Web Page: Available on Avenue to Learn Classes: Tuesday and Thursdays 7:00-10:00 pm TSH B105. (Spring Term) Monday May 4 to Friday June 19. Textbook Elementary Linear Algebra: Applications Version, 11th edition, by Howard Anton and Chris Rorres, published by John Wiley and Sons, Inc. Optionally, the supplement Student Solutions Manual with solutions to odd numbered problems is available separately. An online-only version of the textbook can also be rented from CourseSmart. The 10th edition will also be supported. Topics Vector spaces given by solutions to linear systems. Linear inde-pendence, dimension. Determinants. Eigenvalues, eigenvectors and diagonalization. Complex numbers. Assignments There will be 5 assignments made available through online submission. They will be automatically graded if submitted before the deadline expires. A separate link to this is provided on the course web site. Labs In addition to the assignments, there will be 5 labs which will require the use of Matlab (version 7 or later). These will be submitted using the online lab system. You do not have to attend any scheduled lab