Suppose that T: R → Rm is defined by T(2) A for each of the following matrices below: = D = 0 0 0 -1 0 0 0.5 [40] E = 0 0 02 [201] F = 10 3 01 (a) Rewrite T: R" → R" with correct numbers for m and n for each transformation. What is the domain and codomain of each transformation? (b) Find some way to explain in words and/or graphically what each transformation does as it takes vectors from R to Rm. You might find it t helpful to try out a few input vectors and see what their image is under the transformation. This might be difficult, but an honest effort will give you credit. (c) For the transformation, can you get any output vector? (Any vector in Rm) i. If so, explain why you can get any vector in Rm. ii. If not, give an example of an output vector you can't get with the transformation and explain why.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 5P
Question
Suppose that T: R" → Rm is defined by T() = A for each of the following matrices below:
[40]
E = 0 0
02
0
D = 0 -1
0
0
0 0.5
[201]
F = 10 3 01
(a) Rewrite T: R" → Rm with correct numbers for m and n for each transformation. What is the domain
and codomain of each transformation?
(b) Find some way to explain in words and/or graphically what each transformation does as it takes vectors
from R to Rm. You might find it t helpful to try out a few input vectors and see what their image is
under the transformation. This might be difficult, but an honest effort will give you credit.
(c) For the transformation, can you get any output vector? (Any vector in R™)
i. If so, explain why you can get any vector in Rm.
ii. If not, give an example of an output vector you can't get with the transformation and explain why.
Transcribed Image Text:Suppose that T: R" → Rm is defined by T() = A for each of the following matrices below: [40] E = 0 0 02 0 D = 0 -1 0 0 0 0.5 [201] F = 10 3 01 (a) Rewrite T: R" → Rm with correct numbers for m and n for each transformation. What is the domain and codomain of each transformation? (b) Find some way to explain in words and/or graphically what each transformation does as it takes vectors from R to Rm. You might find it t helpful to try out a few input vectors and see what their image is under the transformation. This might be difficult, but an honest effort will give you credit. (c) For the transformation, can you get any output vector? (Any vector in R™) i. If so, explain why you can get any vector in Rm. ii. If not, give an example of an output vector you can't get with the transformation and explain why.
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