If T: R³ R³ is a linear transformation such that then T = -3 12 -2 *(Q)-E}··(O)-E}··(O)-E] T = 3 T
If T: R³ R³ is a linear transformation such that then T = -3 12 -2 *(Q)-E}··(O)-E}··(O)-E] T = 3 T
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![If \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) is a linear transformation such that
\[
T \left( \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 3 \\ -4 \\ -1 \end{bmatrix}, \quad T \left( \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} -1 \\ 1 \\ 1 \end{bmatrix}, \quad T \left( \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \right) = \begin{bmatrix} -1 \\ 3 \\ 2 \end{bmatrix},
\]
then
\[
T \left( \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} -3 \\ 12 \\ -2 \end{bmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F8572f7d9-2af1-4e5c-9d9b-102c9e2c9479%2F3oij9j_processed.png&w=3840&q=75)
Transcribed Image Text:If \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) is a linear transformation such that
\[
T \left( \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 3 \\ -4 \\ -1 \end{bmatrix}, \quad T \left( \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} -1 \\ 1 \\ 1 \end{bmatrix}, \quad T \left( \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \right) = \begin{bmatrix} -1 \\ 3 \\ 2 \end{bmatrix},
\]
then
\[
T \left( \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} -3 \\ 12 \\ -2 \end{bmatrix}.
\]
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