11. Find a basis for the T-cyclic subspace W of the operator T: V→V generated by the vector 2: V=R³, T(a, b, c) = (a+b+c, 3b, a - c), z = (1,0,0).
11. Find a basis for the T-cyclic subspace W of the operator T: V→V generated by the vector 2: V=R³, T(a, b, c) = (a+b+c, 3b, a - c), z = (1,0,0).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 37EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V.
37. V = P, W is the...
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Answer: Basis for W: ((1, 0, 0), (1,0,1)). Characteristic polynomial for Tw: g(t) = t2 - 2.
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