2012 Nov - ww w ox di a University of Toronto Department of...

This preview shows page 1 - 4 out of 8 pages.

University of TorontoDepartment of MathematicsMAT223H1FLinear Algebra IMidterm Exam IINovember 16, 2012D. Penneys, K. Rafi, D. Rowe, S. Uppal, O. YacobiDuration: 1 hour 30 minutesLast Name:Given Name:Student Number:Tutorial Group:No calculators or other aids are allowed.FOR MARKER USE ONLYQuestionMark1/102/103/104/105/106/5TOTAL/551of8DownloaderID 21140ItemID 7756Item ID: 7756Downloader ID: 21140
[10]1.Given that the matrixA=R=1020301-1010001100000, find a basis for each of the following subspaces:(i)row(A).(ii)col(A).(iii)null(A).Downloader ID: 211401111523121111137120-14has reduced row echelon form(i) We can take the rows inRthat have leading 1s:{(1,0,2,0,3),(0,1,-1,0,1),(0,0,0,1,1)}.(ii) The leading 1s inRoccur in columns 1, 2 and 4, so we can take those columns ofA:{1211,1312,123-1}.(iii) We have free parametersx3=tandx5=s, and an arbitrary element of null(A) is thusof the formx1x2x3x4x5=-2-3ts-ts-tt=s-21100+t-3-10-11.Gaussian elimination guarantees that{-21100,-3-10-11}is a basis for null(A).2of8DownloaderID 21140ItemID 7756Item ID: 7756Item ID: 7756Downloader ID: 21140Item ID: 7756Item ID: 77560Item ID: 7756
[10]

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture