Let E= {e,, ez, ez} be the standard basis for R?, B = {b,, bz, b3} be a basis for a vector space V, and T:R → V be a linear transformation with the property that T(x1. X2. X3) = - (X2 +x3) b, - (x1 + X3) b2 - (x1 + *2) b3- a. Compute T(e,), T(e2), and T(e3). b. Compute [T(e1)]s- [T(e2)]s. and [T(e3)]s- c. Find the matrix for T relative to E and B.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 54EQ
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Let E= {e,, ez, ez} be the standard basis for R?, B = {b,, bz, b3} be a basis for a vector space V, and T:R → V be a linear transformation with the property that
T(x1. X2. X3) = - (X2 +x3) b, - (x1 + X3) b2 - (x1 + *2) b3-
a. Compute T(e,), T(e2), and T(e3).
b. Compute [T(e1)]s- [T(e2)]s. and [T(e3)]s-
c. Find the matrix for T relative to E and B.
Transcribed Image Text:Let E= {e,, ez, ez} be the standard basis for R?, B = {b,, bz, b3} be a basis for a vector space V, and T:R → V be a linear transformation with the property that T(x1. X2. X3) = - (X2 +x3) b, - (x1 + X3) b2 - (x1 + *2) b3- a. Compute T(e,), T(e2), and T(e3). b. Compute [T(e1)]s- [T(e2)]s. and [T(e3)]s- c. Find the matrix for T relative to E and B.
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