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Unformatted text preview: pages 1 4 5 9 10 14 15 19 total scores Exam #1, October 5, Linear Algebra, Spring, 2004, W. Stephen Wilson Name: TA Name and section: NO CALCULATORS, NO PAPERS, SHOW WORK . (1) (4 points) We have two equivalent definitions of a linear transformation T from R n to R m . State both. 2 (2) (3 points) Give the definition of a subspace of R n . (3) (3 points) Give the definition of the kernel of a linear transformation T from R n to R m . 3 (4) (3 points) Show that the kernel of a linear transformation T from R n to R m is a subspace of R n . 4 (5) (3 points) Let L be the line spanned by the vector (1 , , 1). Find the 3 × 3 matrix for the linear transformation for the orthogonal projection to this line proj L : R 3 → L ⊂ R 3 . 5 (6) (3 points) Find a basis for the kernel of the map L of problem (5). 6 (7) (3 points) Find a basis for the image of the map L of problem (5). 7 (8) (3 points) Consider the vectors 1 2 , 1 2 and 1 . Show they form a basis and call that basis B . 8...
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 Spring '08
 HA
 Linear Algebra, Algebra, linear transformation, W. Stephen Wilson

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