### Linear Transformation Problem#### Problem:**22.** Let $ T : \mathbb{R}^2 \to \mathbb{R}^3 $ be a linear transformation such that \[ T(x_1, x_2) = (x_1 - 2x_2, -x_1 + 3x_2, 3x_1 - 2x_2). \]Find $ \mathbf{x} $ such that \[ T(\mathbf{x}) = (-1, 4, 9). \]

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Answered: 22. Let T : R² → R³ be a linear…

22. Let T : R² → R³ be a linear transformation such that T(x1, x2) = (x1 – 2x2, –x1 + 3x2, 3x1 – 2x2). Find x such that T(x) = (-1,4, 9).

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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### Linear Transformation Problem

#### Problem:

**22.** Let $ T : \mathbb{R}^2 \to \mathbb{R}^3 $ be a linear transformation such that
\[ T(x_1, x_2) = (x_1 - 2x_2, -x_1 + 3x_2, 3x_1 - 2x_2). \]
Find $ \mathbf{x} $ such that
\[ T(\mathbf{x}) = (-1, 4, 9). \]

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