Final - Exam I Math 235 March 11, 2009 Name: Instructor 1....

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Unformatted text preview: Exam I Math 235 March 11, 2009 Name: Instructor 1. a: What does it mean for a vector ~v to be in the image of the matrix A = 1 2 1 1 1- 2 ? b: Find a linear equation in v 1 , v 2 and v 3 so that the system A ~w = v 1 v 2 v 3 has a solution. 2. Let the transformation T : R 2 R 2 be the rotation of the plane through / 2. a: Find T 1 and T 1 . In other words, find the matrix of T . b: Find the smallest positive integer k such that T k is the identity transformation. 3. True or false? You must justify your answer to receive credit. a: Let P 3 be the vector space of polynomials in x of degree less than 4. The subset S = { p ( x ) : p ( x ) + xp ( x ) = 0 } is a subspace of P 3 . b: If T : R 4 R 3 is a linear transformation and the vectors 1 1 , 2 3 5 are a basis for im ( T ), then dim ( ker ( T )) = 2. 4. Let V be the vector space spanned by the independent functions cos x and sin x . Let G : V V be the linear transformation defined as...
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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Final - Exam I Math 235 March 11, 2009 Name: Instructor 1....

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