8A The linear representation is given f:R³ R³: (x,y,z) →f(x,y,z)=(x+2y+z, -2x+2z, 4x-4y+4z) i) Find the representation matrix A off with respect to the natural basis of R³ and check if it is orthogonal (we consider the usual inner product here). ii) In the case that A is not orthogonal, then find an orthogonal matrix B resulting from A by normalizing the lines to (we consider the usual inner product here).

8A The linear representation is given f:R³ R³: (x,y,z) →f(x,y,z)=(x+2y+z, -2x+2z, 4x-4y+4z) i) Find the representation matrix A off with respect to the natural basis of R³ and check if it is orthogonal (we consider the usual inner product here). ii) In the case that A is not orthogonal, then find an orthogonal matrix B resulting from A by normalizing the lines to (we consider the usual inner product here).

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 11CM

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