T: R² R³ is a linear transformation for which T hen: T([³])- = 18 T([1]) = 4 and T (1)-[* =
T: R² R³ is a linear transformation for which T hen: T([³])- = 18 T([1]) = 4 and T (1)-[* =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![If \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) is a linear transformation for which
\[ T \left( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 4 \\ 5 \\ 2 \end{bmatrix} \]
and
\[ T \left( \begin{bmatrix} 0 \\ 1 \end{bmatrix} \right) = \begin{bmatrix} -5 \\ 3 \\ 5 \end{bmatrix} \]
then:
\[ T \left( \begin{bmatrix} 5 \\ 4 \end{bmatrix} \right) = \begin{bmatrix} \boxed{\phantom{x}} \\ \boxed{\phantom{x}} \\ \boxed{\phantom{x}} \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F181283bb-83dc-4f09-86f1-fac04e6d4723%2F7e90bf65-4295-47bc-a8ff-9a0b2ef7a04a%2Fwtaucpp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) is a linear transformation for which
\[ T \left( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 4 \\ 5 \\ 2 \end{bmatrix} \]
and
\[ T \left( \begin{bmatrix} 0 \\ 1 \end{bmatrix} \right) = \begin{bmatrix} -5 \\ 3 \\ 5 \end{bmatrix} \]
then:
\[ T \left( \begin{bmatrix} 5 \\ 4 \end{bmatrix} \right) = \begin{bmatrix} \boxed{\phantom{x}} \\ \boxed{\phantom{x}} \\ \boxed{\phantom{x}} \end{bmatrix} \]
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