hich one of the following statements must be true? O dim (im(T)) > dim (ker(T)) OT cannot be an onto transformation A = 0 has only the trivial solution O rank(A) dim (ker(T)) O rank(A) > 3 OT must be a one-to-one transformation =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose T: R5 R³ is a linear transformation, and let A be the matrix that induces this transformation.
Which one of the following statements must be true?
O dim (im(T)) > dim (ker(T))
OT cannot be an onto transformation
O A* = 0 has only the trivial solution
O rank(A) dim (ker(T))
O rank(A) > 3
OT must be a one-to-one transformation
Transcribed Image Text:Suppose T: R5 R³ is a linear transformation, and let A be the matrix that induces this transformation. Which one of the following statements must be true? O dim (im(T)) > dim (ker(T)) OT cannot be an onto transformation O A* = 0 has only the trivial solution O rank(A) dim (ker(T)) O rank(A) > 3 OT must be a one-to-one transformation
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