{[(-101, – 51, – 1) ker(T)
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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![Define the linear transformation \( T \) by \( T(\mathbf{x}) = A\mathbf{x} \).
\[
A = \begin{bmatrix} 1 & -1 & 5 \\ 0 & 1 & 5 \end{bmatrix}
\]
(a) Find the kernel of \( T \). (If there are an infinite number of solutions, use \( t \) as your parameter.)
\[
\ker(T) = \left\{ \begin{pmatrix} -10t \\ -5t \\ -t \end{pmatrix} \right\} \times
\]
*Note: The cross mark indicates an error or incorrect solution. The correct kernel has not been completed.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d7dd770-0f0b-474c-ac91-7886ac60f797%2Fd47b96c9-cfb7-4fbe-8457-e2d4e0628974%2Fl2dteex_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Define the linear transformation \( T \) by \( T(\mathbf{x}) = A\mathbf{x} \).
\[
A = \begin{bmatrix} 1 & -1 & 5 \\ 0 & 1 & 5 \end{bmatrix}
\]
(a) Find the kernel of \( T \). (If there are an infinite number of solutions, use \( t \) as your parameter.)
\[
\ker(T) = \left\{ \begin{pmatrix} -10t \\ -5t \\ -t \end{pmatrix} \right\} \times
\]
*Note: The cross mark indicates an error or incorrect solution. The correct kernel has not been completed.*
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