Problem 6. Consider a linear operator L: R³ R³ given by L(x, y, z) = (2z, y + 3x, 2x - z) for all (x, y, z) € R³. Find a matrix A such that L(v) = Av for every v E R³, where v and L(v) are regarded as column vectors.

Problem 6. Consider a linear operator L: R³ R³ given by L(x, y, z) = (2z, y + 3x, 2x - z) for all (x, y, z) € R³. Find a matrix A such that L(v) = Av for every v E R³, where v and L(v) are regarded as column vectors.

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 17CM

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Question

Problem 6. Consider a linear operator L: R³ R³ given by
→
L(x, y, z) = (2z, y + 3x, 2x - z)
for all (x, y, z) = R³. Find a matrix A such that L(v) = Av for every v E R³, where v and
L(v) are regarded as column vectors.

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