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,...
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0114c863-1109-486a-b8d9-8254bb1b16b5%2F58055675-21d9-4edf-93af-f3e6f18d6100%2Fgflvf7q_processed.jpeg&w=3840&q=75)
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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