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
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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