b1 f(b2) b2 Y Y f(b1) * * Part 2: The matrix of the linear transformation relative to the basis B a. Find the B-coordinate vectors for b₁ and b₂. Enter your answers as coordinate vectors of the form <5,6>. [b1]B= [b2]B= b. Find the B-coordinate vectors for f(b₁) and f(b2). Enter your answers as coordinate vectors of the form <5,6>. [f(b1)]B= [f(b2)]B= c. Find the matrix M for the linear transformation f relative to the basis B in both the domain and codomain. That is, find the matrix M such that [f(v)] = M[v] B. For instance, enter [[1,2], [3,4]] for the matrix 3 4 M=

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 44RE
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b1
f(b2)
b2
Y
Y
f(b1)
*
*
Part 2: The matrix of the linear transformation relative to the basis B
a. Find the B-coordinate vectors for b₁ and b₂. Enter your answers as coordinate vectors of the form <5,6>.
[b1]B=
[b2]B=
b. Find the B-coordinate vectors for f(b₁) and f(b2). Enter your answers as coordinate vectors of the form <5,6>.
[f(b1)]B=
[f(b2)]B=
c. Find the matrix M for the linear transformation f relative to the basis B in both the domain and codomain. That is,
find the matrix M such that [f(v)] = M[v] B. For instance, enter [[1,2], [3,4]] for the matrix
3 4
M=
Transcribed Image Text:b1 f(b2) b2 Y Y f(b1) * * Part 2: The matrix of the linear transformation relative to the basis B a. Find the B-coordinate vectors for b₁ and b₂. Enter your answers as coordinate vectors of the form <5,6>. [b1]B= [b2]B= b. Find the B-coordinate vectors for f(b₁) and f(b2). Enter your answers as coordinate vectors of the form <5,6>. [f(b1)]B= [f(b2)]B= c. Find the matrix M for the linear transformation f relative to the basis B in both the domain and codomain. That is, find the matrix M such that [f(v)] = M[v] B. For instance, enter [[1,2], [3,4]] for the matrix 3 4 M=
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