3y + x ·()-(²) = 2y . Let 0: R³ R³ be the linear mapping given by y (i) Write down the matrix A such that 0v = Av for all v € R³. (ii) Find the kernel of 0, write down a basis for it, and hence calculate the nullity of 0. (iii) Find the image of 0, write down a basis for it, and hence calculate the rank of 0. As a check, verify that the rank-nullity formula holds.

3y + x ·()-(²) = 2y . Let 0: R³ R³ be the linear mapping given by y (i) Write down the matrix A such that 0v = Av for all v € R³. (ii) Find the kernel of 0, write down a basis for it, and hence calculate the nullity of 0. (iii) Find the image of 0, write down a basis for it, and hence calculate the rank of 0. As a check, verify that the rank-nullity formula holds.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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