MAT 272 Assignment 6 - You should be able to tell the...

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MAT 272 Assignment #6 Due: Dec. 10, 2009 1) Let V be a vector space with basis . Let x,y V with coordinates relative to B of {c 1 ,c 2 , …, c n } and {d 1 , d 2 , …d n } respectively. a. Find coordinates for x + y and k x relative to B. b. Are your coordinates unique? Why? 2) Let V be a vector space and a basis for V. For any x V define the coordinate mapping for B as the function where and . Prove that T is a linear transformation. 3) Let . Describe how the rank of A depends on the value of t.
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Unformatted text preview: You should be able to tell the values of t necessary for A to have rank 1, 2 or 3. 4) Let and be two different bases for . a. Find and . b. Let and calculate and 5) Find the eivenvalues for . 6) Let u and v be eigenvectors of the matrix A corresponding to eigenvalues λ 1 and λ 2 . Prove that λ 1 ≠ λ 2 implies u and v are linearly independent....
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