Consider a linear transformation R² → R² described by a matrix 11 18 -6-10 and a non-standard basis B of R²: √₁ A - 2 3 -[B]₁ =B]₁ [3]. = 2 : A. Present a vector w = in the coordinates of B, that is, find [w]. B. Find a matrix B describing the transformation A relative to the basis 3. C. Use this result in order to compute A³ (don't use a calculator!).
Consider a linear transformation R² → R² described by a matrix 11 18 -6-10 and a non-standard basis B of R²: √₁ A - 2 3 -[B]₁ =B]₁ [3]. = 2 : A. Present a vector w = in the coordinates of B, that is, find [w]. B. Find a matrix B describing the transformation A relative to the basis 3. C. Use this result in order to compute A³ (don't use a calculator!).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![1. Consider a linear transformation R² → R² described by a matrix
11 18
-6 -10|
and a non-standard basis B of R²:
A =
A. Present a vector w
4-3 4-N
=
3 in the coordinates of B, that is, find [w].
B. Find a matrix B describing the transformation A relative to the basis B.
C. Use this result in order to compute A³ (don't use a calculator!).
Reminder:
[J-1]
[a b]
=
c d
ad - bc
d
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9225251c-09aa-4cea-8751-a0dbeeb75467%2Ffcb4b684-3201-44fe-be49-036f3b70c1e3%2F3z0mc6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a linear transformation R² → R² described by a matrix
11 18
-6 -10|
and a non-standard basis B of R²:
A =
A. Present a vector w
4-3 4-N
=
3 in the coordinates of B, that is, find [w].
B. Find a matrix B describing the transformation A relative to the basis B.
C. Use this result in order to compute A³ (don't use a calculator!).
Reminder:
[J-1]
[a b]
=
c d
ad - bc
d
a
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