Let L be the linear operator on R³ defined by 2x1 – x2 – X3 L(x) = | 2x2 – x1 – X3 2x3 – X1 – X2 Determine the standard matrix representation A of L, and use A to find L(x) for each of the following vectors x: (a) x= (1, 1, 1)" (b) x = (2, 1, 1)" (c) x = (-5, 3, 2)"

Let L be the linear operator on R³ defined by 2x1 – x2 – X3 L(x) = | 2x2 – x1 – X3 2x3 – X1 – X2 Determine the standard matrix representation A of L, and use A to find L(x) for each of the following vectors x: (a) x= (1, 1, 1)" (b) x = (2, 1, 1)" (c) x = (-5, 3, 2)"

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 16CM

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Question

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Let L be the linear operator on R³ defined by
2x1 – x2 – X3
L(x) = | 2x2 – x1 – X3
2x3 – X1 – X2
Determine the standard matrix representation A of
L, and use A to find L(x) for each of the following
vectors x:
(a) x= (1, 1, 1)"
(b) x = (2, 1, 1)"
(c) x = (-5, 3, 2)"

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