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# HW6 - MA/PH 607 Howell Homework Handout VI A The following...

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MA/PH 607 Howell 10/3/2011 Homework Handout VI A. The following all involve linear operators on a two-dimensional traditional vector space i with standard basis . Try to do all of these problems without refering to the U œ ß e f i j matrix for the operator. 1. What are all the eigenvalues and eigenvectors for the “magnification by 2” operator given by . ` # lparen1 rparen1 v v œ # 2. Consider the vector projection onto , pr , where . What is one a v a i j F0F5h lparen1 rparen1 a œ # mathplus \$ eigenvector corresponding to eigenvalue , and what is one eigenvector - œ" corresponding to eigenvalue ? (Hint: See example 7.1 in the notes.) - œ! 3. Let be the rotation of every vector counterclockwise by a fixed angle Does e ) e ) ) Þ have any eigen-pairs if ? Why or why not? !lessthan lessthan# ) 1 B. The following all involve linear operators on a three-dimensional traditional vector space i with standard basis . Try to do all of these problems without refering to the U œ ß ß e f i j k matrix for the operator.

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