Solve the problem. [1 The columns of 13 = 0 0 O Suppose that T is a linear transformation from R³ into R2 such that T( e₁) = [2]. T( e₂) = [], and T( e3) = [³]. x1 Tx2 = x3 x1 Find a formula for the image of an arbitrary x = x2 in R³. x3 x1 Tx2 = x3 x1 Tx2 - x3 00 1 0 are e₁ = 0 1 5x1+3x2-3x3 -2x1 5x1-2x2 3x1 3x2 + x3 5x1-2x2 3x1 100 + x3 0 , e₂=1, e3= 0 0 O [x1] [5x1+3x2-3x3]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 8E
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Solve the problem.
The columns of l3 = 0
Suppose that T is a linear transformation from R³ into R2 such that
T( e₁) = [5], T( e₂) = [], and T( e3) = [₁].
O
x1
Find a formula for the image of an arbitrary x = x2 in R³.
x3
O
x1
Tx2
x3
x1
Tx2
x3
x1
Tx2
x3
=
[1 0 0
1 0 are e₁ =
0 0 1
5x1 + 3x2-3x3
-2x1
+ x3
5x1-2x2
3x1
3x2 + x3
5x1- 2x2
3x1
5x1 + 3x2-3x3
Tx2 - 3x1
*3
, e2 = 1 e3= 0
1
-2x1 + x3
Transcribed Image Text:Solve the problem. The columns of l3 = 0 Suppose that T is a linear transformation from R³ into R2 such that T( e₁) = [5], T( e₂) = [], and T( e3) = [₁]. O x1 Find a formula for the image of an arbitrary x = x2 in R³. x3 O x1 Tx2 x3 x1 Tx2 x3 x1 Tx2 x3 = [1 0 0 1 0 are e₁ = 0 0 1 5x1 + 3x2-3x3 -2x1 + x3 5x1-2x2 3x1 3x2 + x3 5x1- 2x2 3x1 5x1 + 3x2-3x3 Tx2 - 3x1 *3 , e2 = 1 e3= 0 1 -2x1 + x3
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