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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Consider the linear transformation T: RR³ given by T()= Au, where A is the matrix (a) (b Find rank(T). 23 0 31 1 41 -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
Transcribed Image Text:5. Consider the linear transformation T: RR³ given by T()= Au, where A is the matrix (a) (b Find rank(T). 23 0 31 1 41 -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
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