Let T:R4→R2 be a linear transformation defined by T(x1,x2,x3,x4)=(x1−5x2,x3−7x4). Which of the following statements are true? A. T is one-to-one (or injective). B. T is onto (or surjective). C. T is invertible. D. T−1(0,0)=(0,0,0,0) E. {(5,1,0,0),(0,0,7,1)} is a basis for ker(T). F. {(1,0),(0,1)} is a basis for range(T).

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Answered: Let T:R4→R2 be a linear transformation…

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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Let T:R4→R2 be a linear transformation defined by T(x1,x2,x3,x4)=(x1−5x2,x3−7x4). Which of the following statements are true?

A. T is one-to-one (or injective).
B. T is onto (or surjective).
C. T is invertible.
D. T−1(0,0)=(0,0,0,0)
E. {(5,1,0,0),(0,0,7,1)} is a basis for ker(T).
F. {(1,0),(0,1)} is a basis for range(T).

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