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 transformationO A* = 0 has only the trivial solutionO rank(A) dim (ker(T))O rank(A) > 3OT must be a one-to-one transformation

Here, we use properties of linear transformation. By using properties we Eliminate the wrong option.

Answered: hich one of the following statements…

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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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 =