Determine if the statement is true or false. If it is true, explain why. If it is false, provide a counterexample or an explanation. (a) The transformation T : R³ → R³ defined by T(T1, x2, 03) = (x1 – x2, x² + x3, 03 – 4) is a matrix transformation. (b) If m > n then any linear transformation T : R" → Rm is never one-to-one. (c) If m > n then any linear transformation T : R" > R" is never onto. (d) If B has a column of zeros and A is any matrix for which AB is defined, then AB also has a column of zeros.

Determine if the statement is true or false. If it is true, explain why. If it is false, provide a counterexample or an explanation. (a) The transformation T : R³ → R³ defined by T(T1, x2, 03) = (x1 – x2, x² + x3, 03 – 4) is a matrix transformation. (b) If m > n then any linear transformation T : R" → Rm is never one-to-one. (c) If m > n then any linear transformation T : R" > R" is never onto. (d) If B has a column of zeros and A is any matrix for which AB is defined, then AB also has a column of zeros.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Determine if the statement is true or false. If it is true, explain why. If it is false,
provide a counterexample or an explanation.
(a) The transformation T : R³
→ R³ defined by
T(T1, x2, 03) = (x1 – x2, x² + x3, 03 – 4)
is a matrix transformation.
(b) If m > n then any linear transformation T : R"
→ Rm is never one-to-one.
(c) If m > n then any linear transformation T : R"
> R" is never onto.
(d) If B has a column of zeros and A is any matrix for which AB is defined, then
AB also has a column of zeros.

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