Let f R2 R² be the linear transformation defined by : → Let be two different bases for R². a. Find the matrix [ƒ) / for f relative to the basis B. [f] = b. Find the matrix [f) C( for f relative to the basis C. [f] = c. Find the change-of-basis matrix Sc→B such that [v] B = Sc→B[v]C. SC→B = 88- d. Find the transition matrix SB→c such that [v]c = SB¬c[V] B. Reminder: SBC = (Sc→B)¯¹. SB→C= e. On paper, check that SB→c[f] B/BSc→B = [f]c. 2 4 f(x)= x. 2 C В B0 {(1, 1), (−2, −1)}, = {{−1, −1), (3,2)},
Let f R2 R² be the linear transformation defined by : → Let be two different bases for R². a. Find the matrix [ƒ) / for f relative to the basis B. [f] = b. Find the matrix [f) C( for f relative to the basis C. [f] = c. Find the change-of-basis matrix Sc→B such that [v] B = Sc→B[v]C. SC→B = 88- d. Find the transition matrix SB→c such that [v]c = SB¬c[V] B. Reminder: SBC = (Sc→B)¯¹. SB→C= e. On paper, check that SB→c[f] B/BSc→B = [f]c. 2 4 f(x)= x. 2 C В B0 {(1, 1), (−2, −1)}, = {{−1, −1), (3,2)},
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 11CM
Related questions
Question
![Let f R2 R² be the linear transformation defined by
:
→
Let
be two different bases for R².
a. Find the matrix [ƒ) / for f relative to the basis B.
[f]
=
b. Find the matrix [f) C( for f relative to the basis C.
[f] =
c. Find the change-of-basis matrix Sc→B such that [v] B = Sc→B[v]C.
SC→B =
88-
d. Find the transition matrix SB→c such that [v]c = SB¬c[V] B.
Reminder: SBC = (Sc→B)¯¹.
SB→C=
e. On paper, check that SB→c[f] B/BSc→B = [f]c.
2
4
f(x)=
x.
2
C
В
B0
{(1, 1), (−2, −1)},
=
{{−1, −1), (3,2)},](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75248f5c-2719-4287-81a4-5e6a0d930fd1%2F8127511a-e6a1-4de0-9636-45627863e82a%2Fszvty6jh_processed.png&w=3840&q=75)
Transcribed Image Text:Let f R2 R² be the linear transformation defined by
:
→
Let
be two different bases for R².
a. Find the matrix [ƒ) / for f relative to the basis B.
[f]
=
b. Find the matrix [f) C( for f relative to the basis C.
[f] =
c. Find the change-of-basis matrix Sc→B such that [v] B = Sc→B[v]C.
SC→B =
88-
d. Find the transition matrix SB→c such that [v]c = SB¬c[V] B.
Reminder: SBC = (Sc→B)¯¹.
SB→C=
e. On paper, check that SB→c[f] B/BSc→B = [f]c.
2
4
f(x)=
x.
2
C
В
B0
{(1, 1), (−2, −1)},
=
{{−1, −1), (3,2)},
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