Problem 6. Write a matrix for the linear transformation T: R³ → R³ satisfying TO) -()· () - () - () 0 = T1 2 T 0
Problem 6. Write a matrix for the linear transformation T: R³ → R³ satisfying TO) -()· () - () - () 0 = T1 2 T 0
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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![**Problem 6:** Write a matrix for the linear transformation \( T: \mathbb{R}^3 \to \mathbb{R}^3 \) satisfying
\[
T \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 1 \\ 5 \end{pmatrix} , \quad T \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} , \quad T \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \\ 4 \end{pmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F672bf286-8abe-4b07-9ca1-0d5b2612956c%2Fdd046f94-124a-427d-8fa9-fb5e1145dbd1%2Fzv4k0sfx_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 6:** Write a matrix for the linear transformation \( T: \mathbb{R}^3 \to \mathbb{R}^3 \) satisfying
\[
T \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 1 \\ 5 \end{pmatrix} , \quad T \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} , \quad T \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \\ 4 \end{pmatrix}.
\]
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