1: Define a map T : R' → R³ byx – 2wx + 3y – z + 4wTa) Show that T is linear.b) Find the matrix of Tb) Determine if T is injective. If not, describe the set of vectors xfor which T(x) = 0.c) Determine if T is onto. If so, for any given b = b2|b3xE R' such that T(x) = b. That is, describe coordinates of xfindusing b1, b2 and b3.

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1: Define a map T : R' → R³ by x - 2w x+ 3y – z + 4w z - w w a) Show that T is linear. b) Find the matrix of T b) Determine if T is injective. If not, describe the set of vectors x for which T(x) = 0.

1: Define a map T : R' → R³ by x - 2w x+ 3y – z + 4w z - w w a) Show that T is linear. b) Find the matrix of T b) Determine if T is injective. If not, describe the set of vectors x for which T(x) = 0.

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

1: Define a map T : R' → R³ by
x – 2w
x + 3y – z + 4w
T
a) Show that T is linear.
b) Find the matrix of T
b) Determine if T is injective. If not, describe the set of vectors x
for which T(x) = 0.
c) Determine if T is onto. If so, for any given b = b2
|b3
xE R' such that T(x) = b. That is, describe coordinates of x
find
using b1, b2 and b3.

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