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 \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) is a linear map, and
\[
T \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 1 \end{bmatrix}, \quad T \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 5 \end{bmatrix}, \quad \text{and} \quad T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}.
\]
Then
\[
T \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} = \ldots
\]
Options:
1. \(\ldots \begin{bmatrix} 7 \\ 5 \\ 1 \end{bmatrix}\)
2. \(\ldots \begin{bmatrix} 5 \\ 4 \\ 1 \end{bmatrix}\)
3. \(\ldots \begin{bmatrix} 2 \\ 3 \\ 9 \end{bmatrix}\)
4. \(\ldots \begin{bmatrix} 8 \\ 7 \\ 6 \end{bmatrix}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0114c863-1109-486a-b8d9-8254bb1b16b5%2Fbf2f4ba6-0d47-4676-9dd1-2104c46f4e01%2Ftbrgman_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) is a linear map, and
\[
T \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 1 \end{bmatrix}, \quad T \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 5 \end{bmatrix}, \quad \text{and} \quad T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}.
\]
Then
\[
T \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} = \ldots
\]
Options:
1. \(\ldots \begin{bmatrix} 7 \\ 5 \\ 1 \end{bmatrix}\)
2. \(\ldots \begin{bmatrix} 5 \\ 4 \\ 1 \end{bmatrix}\)
3. \(\ldots \begin{bmatrix} 2 \\ 3 \\ 9 \end{bmatrix}\)
4. \(\ldots \begin{bmatrix} 8 \\ 7 \\ 6 \end{bmatrix}\)
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