Given a linear operator T: R³ R³ with the bases R and S where R = OG)·()} and S is the standard basis for R³. a) Find the transition matrix from S to R. b) [1 1 01 0, find the matrix for T relative to basis R, [T]R- 2 1 31 If [T] 0 2 = c) If the coordinate vector u with respect to S is [u]s - ³1. = calculate [T(u)]R-
Given a linear operator T: R³ R³ with the bases R and S where R = OG)·()} and S is the standard basis for R³. a) Find the transition matrix from S to R. b) [1 1 01 0, find the matrix for T relative to basis R, [T]R- 2 1 31 If [T] 0 2 = c) If the coordinate vector u with respect to S is [u]s - ³1. = calculate [T(u)]R-
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 18E: Prove part b of Theorem 1.35.
Theorem 1.35 Special Properties of
Let be an arbitrary matrix...
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![Given a linear operator T: R³ R³ with the bases R and S where R =
OG)·()}
and S is the standard basis for R³.
a) Find the transition matrix from S to R.
b)
[1 1 01
If [T] 0 2 0, find the matrix for T relative to basis R, [T]R-
=
[2
1 31
c)
If the coordinate vector u with respect to S is [u]s
- ³1.
=
calculate [T(u)]R-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ad01f60-4219-492f-ba73-b52c85c2a06b%2F7d4210ca-34cd-4e60-9cfc-a6f1fe0917b3%2Fyan2ed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a linear operator T: R³ R³ with the bases R and S where R =
OG)·()}
and S is the standard basis for R³.
a) Find the transition matrix from S to R.
b)
[1 1 01
If [T] 0 2 0, find the matrix for T relative to basis R, [T]R-
=
[2
1 31
c)
If the coordinate vector u with respect to S is [u]s
- ³1.
=
calculate [T(u)]R-
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