Solve the problem. 0 E --6 0 1 The columns of 13 are e₁= e2= e3 0 Suppose that T is a linear transformation from R³ into R² such that -[-$]. -[3] T( e₁) - , and T( e3) = -[3] X1 Find a formula for the image of an arbitrary x= O x1 6x1-3x27 Tx2 = 2x1 x3 2x2 + x3 Ox1 6x1+2x2-2x3 -3x1 + x3 6x1-3x2 2x1 6x1+2x2-2x3 -3x1 + x3 Tx2 = x3 Ox1 Tx2= x3 Ox1 Tx2 - 2x1 , T(e₂) = 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Solve the problem.
1
00
[1]. -18].
0
10
The columns of 13 =
are e₁=
e2=
0
0
Suppose that T is a linear transformation from R³ into R² such that
-[3]
T(e₁) =
[1]
, T(e₂) =
and T(3) =
8-
Find a formula for the image of an arbitrary x=
Ox1
6x1-3x2
Tx2
2x1
x3
2x2 + x3
Ox1
6x1+2x2-2x3
Tx2
-3x1
x3
x3
x1
6x1-3x2
Tx2
2x1
x3
x1 6x1+2x2-2x3
Tx2 = 2x1
x3
-3x1+x3
e3 =
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Transcribed Image Text:Solve the problem. 1 00 [1]. -18]. 0 10 The columns of 13 = are e₁= e2= 0 0 Suppose that T is a linear transformation from R³ into R² such that -[3] T(e₁) = [1] , T(e₂) = and T(3) = 8- Find a formula for the image of an arbitrary x= Ox1 6x1-3x2 Tx2 2x1 x3 2x2 + x3 Ox1 6x1+2x2-2x3 Tx2 -3x1 x3 x3 x1 6x1-3x2 Tx2 2x1 x3 x1 6x1+2x2-2x3 Tx2 = 2x1 x3 -3x1+x3 e3 = No new data to save last
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