Let T : P 2 R → P 2 R be defined by T p x ...

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University of Toronto Department of Mathematics MAT224H1S Linear Algebra II Midterm Examination I Feb. 9, 2011 Y. Burda, S. Uppal Duration: 1 hour 30 minutes Last Name: Given Name: Student Number: Tutorial Code: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /6 6 /4 TOTAL /50 1 of 8 DownloaderID 24460 ItemID 15891 Item ID: 15891 Downloader ID: 24460 Item ID: 15891 Downloader ID: 24460 Downloader ID: 24460
1. Let T : P 2 ( R ) P 2 ( R ) be defined by T ( p ( x )) = p ( x 1) . (a) Show that T is a linear operator. (b) Find the matrix of T relative to the basis α = { 1 , 1 + x, 1 + x + x 2 } of P 2 ( R ). Solution: ItemID 15891
2 of 8 Item ID: 15891
2. Is the set { ( i, 1 , 2 i ) , (1 , 1+ i, i ) , (1 , 3+5 i, 4+3 i ) } a basis for C 3 ? Justify your answer.

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