B ³ = {( ¹₂ ). ( ³ ) } Tv Av where A is a matrix is a basis of R2. T: R2 R2 is a linear transformation given by - [32] 02 A =
B ³ = {( ¹₂ ). ( ³ ) } Tv Av where A is a matrix is a basis of R2. T: R2 R2 is a linear transformation given by - [32] 02 A =
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
![4. B =
{(1)-(3)}
2
5
Tv - Av where A is a matrix
is a basis of R2. T: R² R2 is a linear transformation given by
(a) Use definition to find [T]
(b) Use definition to find [T]
2
= [83]
02
A =
the matrix of T under the basis B.
the matrix of T under the standard basis E.
(c) Compute PE+B and PB-E-
(d) Use Part (b) and (c) to find [T]B the matrix of T under the basis B. Compare your
answer with that of Part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67429e19-8d15-47bc-bbfe-dfa923849540%2F639a7927-7c2f-4a06-a8a8-99bef0b0bd5a%2Fl0nl9n7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. B =
{(1)-(3)}
2
5
Tv - Av where A is a matrix
is a basis of R2. T: R² R2 is a linear transformation given by
(a) Use definition to find [T]
(b) Use definition to find [T]
2
= [83]
02
A =
the matrix of T under the basis B.
the matrix of T under the standard basis E.
(c) Compute PE+B and PB-E-
(d) Use Part (b) and (c) to find [T]B the matrix of T under the basis B. Compare your
answer with that of Part (a).
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Step 1: Define Matrix representation of T w.r.t orderd basis
VIEWStep 2: Determine the required matrix w.r.t. the basis B
VIEWStep 3: Use definition
VIEWStep 4: Determine the required matrix w.r.t. the basis E
VIEWStep 5: Determine the transition matrix from E to B
VIEWStep 6: Determine the transition matrix from B to E
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