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[1 The columns of 3 = 0 O Suppose that T is a linear transformation from R³ into R² such that T(e₁) = ₁)-[2]. Te₂)-[6], and T(3)-[i] O 0 0] 1 0 are e₁ = 001 Find a formula for the image of an arbitrary x = x2 in ³. x3 [x1] 3x1-2x2] Tx2 = 2x1 x1 Tx2 = 2x1 Tx2 = 4x2 + x3 3x1+2x2-4x3 -2x1 + x3 -13] |:| ,e2 3x1-2x2 2x1 e3 3x1+2x2- 4x3 -2x1 + x3

[1 The columns of 3 = 0 O Suppose that T is a linear transformation from R³ into R² such that T(e₁) = ₁)-[2]. Te₂)-[6], and T(3)-[i] O 0 0] 1 0 are e₁ = 001 Find a formula for the image of an arbitrary x = x2 in ³. x3 [x1] 3x1-2x2] Tx2 = 2x1 x1 Tx2 = 2x1 Tx2 = 4x2 + x3 3x1+2x2-4x3 -2x1 + x3 -13] |:| ,e2 3x1-2x2 2x1 e3 3x1+2x2- 4x3 -2x1 + x3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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[:] Suppose that T is a linear transformation from ³ into ² such that 3 -[-2]. (₂) - [8].a T -[2], and T(3) = [1] The columns of k T(e₁) O *1 Tx2 = 2x1 x3 *1 TX2 002 1 0 0 0 Tx2 = *3 3x1-2x2] Tx2 = 2x1 001 Find a formula for the image of an arbitrary x= x2 in ³. 4x2 + x3 1 0 are e₁ 3x1 + 2x2 - 4x3 -2x1 + x3 3x1-2x1 2x1 3x1 + 2x2-4x3 -2x1 wwww + X3 x3 0 e2 ез 0 akan wwwwww.
Transcribed Image Text:[:] Suppose that T is a linear transformation from ³ into ² such that 3 -[-2]. (₂) - [8].a T -[2], and T(3) = [1] The columns of k T(e₁) O *1 Tx2 = 2x1 x3 *1 TX2 002 1 0 0 0 Tx2 = *3 3x1-2x2] Tx2 = 2x1 001 Find a formula for the image of an arbitrary x= x2 in ³. 4x2 + x3 1 0 are e₁ 3x1 + 2x2 - 4x3 -2x1 + x3 3x1-2x1 2x1 3x1 + 2x2-4x3 -2x1 wwww + X3 x3 0 e2 ез 0 akan wwwwww.
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