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Suppose that T: R³ R³ is a linear map, and ... T2 = ·-· ----· 2 and T Then B T 3 25 13 3 10 36 23 78 T 0 =

Suppose that T: R³ R³ is a linear map, and ... T2 = ·-· ----· 2 and T Then B T 3 25 13 3 10 36 23 78 T 0 =

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Suppose that \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) is a linear map, and \[ T \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}, \quad T \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 5 \end{bmatrix}, \quad \text{and} \quad T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}. \] Then \[ T \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix} = \ldots \] - \(\ldots\) \(\begin{bmatrix} 25 \\ 13 \\ -9 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} 3 \\ 6 \\ 10 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} 36 \\ 23 \\ -4 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} -5 \\ 78 \\ -1 \end{bmatrix}\) **Explanation:** This problem discusses a mathematical concept where a function \( T \) is applied to various vectors in \( \mathbb{R}^3 \). The goal is to determine the outcome of applying this function \( T \) to the vector \(\begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}\) based on given transformations of other vectors.
Transcribed Image Text:Suppose that \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) is a linear map, and \[ T \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}, \quad T \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 5 \end{bmatrix}, \quad \text{and} \quad T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}. \] Then \[ T \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix} = \ldots \] - \(\ldots\) \(\begin{bmatrix} 25 \\ 13 \\ -9 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} 3 \\ 6 \\ 10 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} 36 \\ 23 \\ -4 \end{bmatrix}\) - \(\ldots\) \(\begin{bmatrix} -5 \\ 78 \\ -1 \end{bmatrix}\) **Explanation:** This problem discusses a mathematical concept where a function \( T \) is applied to various vectors in \( \mathbb{R}^3 \). The goal is to determine the outcome of applying this function \( T \) to the vector \(\begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}\) based on given transformations of other vectors.
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