12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal. 12: Find a basis B for R', such th...

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Question

12: Find a basis B for R, such that the matrix for the linear transformation T: R R, T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative

Answer 1

Answer #1

GivenT 2 る .3 Eigenvector 20r for Az- R2-R 2 3x1-233-0 is 1-2 -is-an-eigenvecher coresponding λ 2 3 12 거 Now B. ence s an diagonal Hence Basis B

Answer 2

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