5. Consider the linear transformation T: R → R³ given by T()= Au, where A is the matrix (a) (b Find rank(T). 23 0 31 1 4 1 -12 1 Find a subset of the columns of A which span the image of T. (For regularity, each column picked can't be written as a linear combination of the columns that came before) might help) Is T a one-to-one function? Why? (Hint: The rank-nullity theorem

5. Consider the linear transformation T: R → R³ given by T()= Au, where A is the matrix (a) (b Find rank(T). 23 0 31 1 4 1 -12 1 Find a subset of the columns of A which span the image of T. (For regularity, each column picked can't be written as a linear combination of the columns that came before) might help) Is T a one-to-one function? Why? (Hint: The rank-nullity theorem

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...

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