For each of the following linear operators T on a vector space V and ordered bases ẞ, compute [T], and determine whether ẞ is a basis consisting of eigenvectors of T. a (a) V = R², T = (199 10a- 6b and B = " {(2), (3)} 17a10b (b) VP1(R), T(a + b) = (6a-6b) + (12a - 11b)x, and B={3+4x, 2+3x} (c) V = R³, T a - 3a+26 2c\ -4a-3b+2c TO) -(+ C and " B = (d) VP2(R), T(a + bx + cx²) = (-4a+26-2c) - (7a+3b+7c)x+(7a+b+5c)x², and ẞ {x x2, -1+x2,-1-x+x2} = -
For each of the following linear operators T on a vector space V and ordered bases ẞ, compute [T], and determine whether ẞ is a basis consisting of eigenvectors of T. a (a) V = R², T = (199 10a- 6b and B = " {(2), (3)} 17a10b (b) VP1(R), T(a + b) = (6a-6b) + (12a - 11b)x, and B={3+4x, 2+3x} (c) V = R³, T a - 3a+26 2c\ -4a-3b+2c TO) -(+ C and " B = (d) VP2(R), T(a + bx + cx²) = (-4a+26-2c) - (7a+3b+7c)x+(7a+b+5c)x², and ẞ {x x2, -1+x2,-1-x+x2} = -
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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