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University of Toronto Department of Mathematics MAT224H1F Linear Algebra II Midterm Examination October 23, 2012 S. Uppal Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Tutorial Group: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /10 6 /10 TOTAL /60 1 of 7 DownloaderID 24460 ItemID 15891 Item ID: 15891 Downloader ID: 24460 Downloader ID: 24460 Item ID: 15891 Item ID: 15891 Item ID: 15891 Downloader ID: 24460 Item ID: 15891 Downloader ID: 24460 Downloader ID: 24460
[10] 1. Let T : R 3 R 2 be the linear transformation that has the matrix 2 3 1 1 2 1 relative to the bases α = { (1 , 1 , 1) , (0 , 1 , 0) , (1 , 0 , 0) } of R 3 and β = { (3 , 2) , (2 , 1) } of R 2 . Find T ( x, y, z ) for any ( x, y, z ) R 3 . Item ID: 15891 Item ID: 15891
2 of 7 ItemID 15891 Downloader ID: 24460 Downloader ID: 24460 Item ID: 15891 Downloader ID: 24460
[10] 2. Let T : P 2 ( R ) R 3 be the linear transformation defined by T ( a + bx + cx 2 ) = ( a + b, b + c, a c ) . Find bases for the kernel and image of T .

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