Let V be a vector space with a basis B= (b,, ., b,, let W be the same space V with a basis C= (c,, .., C), and let I be the identity transformation I: V+W. Find the matrix for I re For each j, I(b)) = |and ['(b) ]c=| Combine these identities with the definition of th atrix to find the matrix for I relative to B and C. M =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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The answer options for the first fill-in-the-blank part of the question are the following:

a) [I(bj]c 

2) bj

3) [bj]c

Let V be a vector space with a basis B= (b,, ., b,, let W be the same space V with a basis C=.
c, and let I be the identity transformation I: V-W. Find the matrix for I relative to B and C.
.....
For each j, I(
j.! (b)) =
and ['(b) ]c=|
Combine these identities with the definition of the transformation matrix to find the matrix for I relative to B and C.
M=
...
b, b2
...
C, C2
...
[
[]s [°2]8
...
Transcribed Image Text:Let V be a vector space with a basis B= (b,, ., b,, let W be the same space V with a basis C=. c, and let I be the identity transformation I: V-W. Find the matrix for I relative to B and C. ..... For each j, I( j.! (b)) = and ['(b) ]c=| Combine these identities with the definition of the transformation matrix to find the matrix for I relative to B and C. M= ... b, b2 ... C, C2 ... [ []s [°2]8 ...
Let V be a vector space with a basis B= (b,, ., b,, let W be the same space V with a basis C= (c,,.., c,, and let I be the identity transformation I: V-W. Find the matrix for I relative to B and C.
For each j, I(b) =
and ['(b)]c=
Combine these identities with the definition of the
atrix to find the matrix for I relative to B and C.
M=
b-
Transcribed Image Text:Let V be a vector space with a basis B= (b,, ., b,, let W be the same space V with a basis C= (c,,.., c,, and let I be the identity transformation I: V-W. Find the matrix for I relative to B and C. For each j, I(b) = and ['(b)]c= Combine these identities with the definition of the atrix to find the matrix for I relative to B and C. M= b-
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