Let T: R2→R2 be a linear transformation such that T (x1,X2) = (X1 + X2, 3x1 + 5x2) . Find x such that T(x) = (2,0). X =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let \( T: \mathbb{R}^2 \to \mathbb{R}^2 \) be a linear transformation such that \( T(x_1, x_2) = (x_1 + x_2, 3x_1 + 5x_2) \). Find \( \mathbf{x} \) such that \( T(\mathbf{x}) = (2, 0) \).

\[
\mathbf{x} = \begin{bmatrix} 
\Box \\ 
\Box 
\end{bmatrix}
\]

**Explanation:**

The problem involves a linear transformation \( T \) from \( \mathbb{R}^2 \) to \( \mathbb{R}^2 \). This transformation is defined by the formula:

\[ 
T(x_1, x_2) = (x_1 + x_2, 3x_1 + 5x_2) 
\]

You are asked to find the vector \( \mathbf{x} \) such that when this transformation is applied, it results in the vector \( (2, 0) \). The vector \( \mathbf{x} \) is represented as a column matrix with two placeholders for elements.
Transcribed Image Text:Let \( T: \mathbb{R}^2 \to \mathbb{R}^2 \) be a linear transformation such that \( T(x_1, x_2) = (x_1 + x_2, 3x_1 + 5x_2) \). Find \( \mathbf{x} \) such that \( T(\mathbf{x}) = (2, 0) \). \[ \mathbf{x} = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \] **Explanation:** The problem involves a linear transformation \( T \) from \( \mathbb{R}^2 \) to \( \mathbb{R}^2 \). This transformation is defined by the formula: \[ T(x_1, x_2) = (x_1 + x_2, 3x_1 + 5x_2) \] You are asked to find the vector \( \mathbf{x} \) such that when this transformation is applied, it results in the vector \( (2, 0) \). The vector \( \mathbf{x} \) is represented as a column matrix with two placeholders for elements.
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