1) Let T=la + 1b+5c+(-1)d-la + Ob + (-4) c+ 3d7a+ 4b +32c +(-13) d7a+ 4b +32c + (-13) d[-la+(-2) b+ (-6) c+(-1)d]Then a basis for (Range(T)) would be:la +(-1) b + (-1) c+4d+7e2a + (-1) b+ 0c + 5d +9e2) Let T(a + bx + cx² + dx²³ + ex¹) = -7a+ 4b + 1c + (-19) d + (-34) e2a + 0b +3c+ld + 3ela + 1b +5c+(-3) d + (-3) eThen a basis for (Range(T))+ would be:

Answered: Image /qna-images/answer/a2866b1f-aef3-4fec-8a8e-d41aa18a5a93.jpg

1) Let T = la + 1b+5c+(-1)d -la+0b+ (-4) c+3d 7a+ 4b +32c +(-13) d 7a+ 4b +32c +(-13) d -la+(-2) b+ (-6) c+(-1)d] Then a basis for (Range(T)) would be: la +(-1) b+(-1) c+4d+7e 2a + (-1) b+0c + 5d +9e 2) Let T(a+b - cx² + dx³ + ex) = -7a+ 4b + 1c +(-19) d + (-34) e 2a +0b+3c+ld + 3e la + lb + 5c+(-3)d+(-3) e Then a basis for (Range(T))+ would be:

1) Let T = la + 1b+5c+(-1)d -la+0b+ (-4) c+3d 7a+ 4b +32c +(-13) d 7a+ 4b +32c +(-13) d -la+(-2) b+ (-6) c+(-1)d] Then a basis for (Range(T)) would be: la +(-1) b+(-1) c+4d+7e 2a + (-1) b+0c + 5d +9e 2) Let T(a+b - cx² + dx³ + ex) = -7a+ 4b + 1c +(-19) d + (-34) e 2a +0b+3c+ld + 3e la + lb + 5c+(-3)d+(-3) e Then a basis for (Range(T))+ would be:

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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