Section 5.1: 3(d)only! 3. For each of the following linear operators T on a vector space V andordered bases ẞ, compute [T]s, and determine whether ẞ is a basisconsisting of eigenvectors of T.a(a) V = R², T= (199-10a 6b17a10b, and 3 ={(2), (3)}(b) VP1(R), T(a + bx)B = {3+ 4x, 2+3x}a(c) V R3, Tb=(O) -(C=-(6a 6b)+(12a - 11b)x, and3a+2b 2c\--4a-3b+2c, and-{(0)·(9)·0))2(d) VP2(R), T(a + bx + cx²)=-C(-4a2b2c) - (7a+3b+7c)x + (7a+b+5c)x²,and ẞ= {x-x², -1 + x², -1- x + x ² }(e) VP3(R), T(a + bx + cx² + dx³)=-d+(-c+d)x + (a + b − 2c)x² + (b + c = 2d) x³,-and ẞ {1x+x3,1 + x², 1, x + x2}=b)---7a-4b+4c-4d b-8a 4b+5c 4d d--(f) V = M2x2 (R), T ( a b )c¿).andβ- {( ) ( ) ( ) (9)}1 0""2021

d. Given, a linear operator on a vector space defined by and and .It is required to compute…

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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