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University of Toronto Department of Mathematics MAT223H1S Linear Algebra I Midterm Exam II March 21, 2014 A. Garcia-Raboso, C. Kent, F. Murnaghan, K. Tyros, S. Uppal Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Email (@mail.utoronto.ca): Instructions : No calculators or other aids are allowed . Show all your work and justify your answers . You may use the back of each page for rough work but all your answers must be written on the front of each page . 1 of 14 DownloaderID 21140 ItemID 10984 Item ID: 10984 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 Item ID: 10984 Item ID: 10984 Downloader ID: 21140 Item ID: 10984
1. Suppose you are given that the matrix A = R = 1 0 5 0 22 1 0 1 1 0 5 0 0 0 0 1 2 0 . [1] (a) Determine the rank of A . [9] (b) Find a basis for each of the following three subspaces: 1 3 2 5 3 1 2 7 3 7 5 2 3 11 4 10 9 3 has reduced echelon form (i) row( A ), (ii) col( A ), and (iii) null( A ). Solution: DownloaderID 21140
2. Consider the subset W = x 2 x 3 2 . [5] (a) Show that W is a subspace of R 3 braceleftBig x 1 R 3 | x 1 3 = x 2 4 = x 3 bracerightBig
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