Jn is simply an nxn matrix with only ones inside. Consider the linear transformation J, : Fn → F", with notations being as in Q5, and F is an arbitrary field.(a) Describe the kernel and the image of Jn.(b) Use this to show that Jn is diagonalisable when n + 0 in F.

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(a) Describe the kernel and the image of Jn. (b) Use this to show that J, is diagonalisable when n # 0 in F.

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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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Jn is simply an nxn matrix with only ones inside.

Consider the linear transformation J, : Fn → F", with notations being as in Q5, and F is an arbitrary field.
(a) Describe the kernel and the image of Jn.
(b) Use this to show that Jn is diagonalisable when n + 0 in F.

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