1 - 5 - 15 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = and b = 24 -4 11 ..... Find a single vector x whose image under T is b. x-0 X =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If \( T \) is defined by \( T(\mathbf{x}) = A\mathbf{x} \), find a vector \( \mathbf{x} \) whose image under \( T \) is \( \mathbf{b} \), and determine whether \( \mathbf{x} \) is unique. Let 

\[ A = \begin{bmatrix} 1 & -5 & -15 \\ -4 & 11 & 24 \end{bmatrix} \]

and 

\[ \mathbf{b} = \begin{bmatrix} -2 \\ -1 \end{bmatrix} \].

---

Find a single vector \( \mathbf{x} \) whose image under \( T \) is \( \mathbf{b} \).

\[ \mathbf{x} = \boxed{} \]
Transcribed Image Text:If \( T \) is defined by \( T(\mathbf{x}) = A\mathbf{x} \), find a vector \( \mathbf{x} \) whose image under \( T \) is \( \mathbf{b} \), and determine whether \( \mathbf{x} \) is unique. Let \[ A = \begin{bmatrix} 1 & -5 & -15 \\ -4 & 11 & 24 \end{bmatrix} \] and \[ \mathbf{b} = \begin{bmatrix} -2 \\ -1 \end{bmatrix} \]. --- Find a single vector \( \mathbf{x} \) whose image under \( T \) is \( \mathbf{b} \). \[ \mathbf{x} = \boxed{} \]
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