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Suppose that T: IR" → R is defined by T(x) = Ax for each of the matrices listed below. For each given matrix, answer the following questions: 300 4 0 201 D=0-1 0 E=00 F = 0 3 0 [0 0 0.5 02 a. Rewrite T: RT → RT with correct numbers for m and n filled in for each matrix. What is the domain of T? What is the codomain of T? b. Find some way to explain in words and/or graphically what this transformation does in taking vectors from R" to Rm. You might find it 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 find two different input vectors that will give the same output vector? d. i. If so, give an example. ii. If not, why do you think it isn't possible? For the transformation, can you get any output vector? (Any vector in R™) i. If so, explain why you can get any vector in IR™ ii. If not, give an example of an output vector you can't get with the transformation and explain why.

Suppose that T: IR" → R is defined by T(x) = Ax for each of the matrices listed below. For each given matrix, answer the following questions: 300 4 0 201 D=0-1 0 E=00 F = 0 3 0 [0 0 0.5 02 a. Rewrite T: RT → RT with correct numbers for m and n filled in for each matrix. What is the domain of T? What is the codomain of T? b. Find some way to explain in words and/or graphically what this transformation does in taking vectors from R" to Rm. You might find it 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 find two different input vectors that will give the same output vector? d. i. If so, give an example. ii. If not, why do you think it isn't possible? For the transformation, can you get any output vector? (Any vector in R™) i. If so, explain why you can get any vector in IR™ ii. If not, give an example of an output vector you can't get with the transformation and explain why.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 77E
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Suppose that T: IR" → R is defined by T(x) = Ax for each of the matrices listed below. For each given matrix, answer the following questions: 300 4 0 201 D=0-1 0 E=00 F = 0 3 0 [0 0 0.5 02 a. Rewrite T: RT → RT with correct numbers for m and n filled in for each matrix. What is the domain of T? What is the codomain of T? b. Find some way to explain in words and/or graphically what this transformation does in taking vectors from R" to Rm. You might find it 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 find two different input vectors that will give the same output vector? d. i. If so, give an example. ii. If not, why do you think it isn't possible? For the transformation, can you get any output vector? (Any vector in R™) i. If so, explain why you can get any vector in IR™ 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: IR" → R is defined by T(x) = Ax for each of the matrices listed below. For each given matrix, answer the following questions: 300 4 0 201 D=0-1 0 E=00 F = 0 3 0 [0 0 0.5 02 a. Rewrite T: RT → RT with correct numbers for m and n filled in for each matrix. What is the domain of T? What is the codomain of T? b. Find some way to explain in words and/or graphically what this transformation does in taking vectors from R" to Rm. You might find it 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 find two different input vectors that will give the same output vector? d. i. If so, give an example. ii. If not, why do you think it isn't possible? For the transformation, can you get any output vector? (Any vector in R™) i. If so, explain why you can get any vector in IR™ ii. If not, give an example of an output vector you can't get with the transformation and explain why.
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