1 ál v = (6, 1, 1), w = (3, 5) A = %3D 2
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.9: Modeling With Equations
Problem 5E
Related questions
Question
Define the linear transformation T: Rn→Rm by T(v) = Av. Use the matrix A to (a) determine the dimensions of Rn and Rm, (b) find the image of v, and (c) find the preimage of w.
![1
ál v = (6, 1, 1), w = (3, 5)
A =
%3D
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2f5323-d4a3-486a-9e54-b278a0956f69%2F512d957c-f88c-47a7-980b-9dd1fb45e448%2Fbxr3p3o.png&w=3840&q=75)
Transcribed Image Text:1
ál v = (6, 1, 1), w = (3, 5)
A =
%3D
2
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1 Given:
Let T be a linear transformation such that .
, ,
Step 2 (a)
To determine: The dimensions of and .
Here v shows the preimage.
The dimension of v is 3.
Thus, the dimension for is 3 ( )
Also, w is the image.
The dimension of w is 2.
Thus, the dimension for is 2 ( )
Step 3 (b)
To find: The image of v.
Let w be the image of v.
Then,
The image of v is .
Step by step
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