1. Let ei , e2 = and e3 = Suppose that T : R³ →Rª is a linear transformation 1 such that 1 T(e1): 2 T(e2) = T(e3) -1 (a) Find the standard matrix for T. 3 4 (b) Find an x E R³ such that T (x)= b, where b = 1 %3| 2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 4EQ: In Exercises 1-12, determine whether T is a linear transformation. 4. defined by , where B is a...
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1. Let ej
and e3
Suppose that T : R³ → R* is a linear transformation
such that
1
1
T(e1)
T(e2) =
T(e3) =
(a) Find the standard matrix for T.
3
(b) Find an x ER' such that T(x) = b, where b =
1
2
Transcribed Image Text:1. Let ej and e3 Suppose that T : R³ → R* is a linear transformation such that 1 1 T(e1) T(e2) = T(e3) = (a) Find the standard matrix for T. 3 (b) Find an x ER' such that T(x) = b, where b = 1 2
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