Let A = 1 6 0 7 12 15 3 5 0 4 36 3 6 0624 " b= 4 9 k (a) Find condition on k E R such that Ax = b, x € R” is solvable. (b) Find all solutions when condition in a) holds.
Let A = 1 6 0 7 12 15 3 5 0 4 36 3 6 0624 " b= 4 9 k (a) Find condition on k E R such that Ax = b, x € R” is solvable. (b) Find all solutions when condition in a) holds.
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 Statement:**
Let
\[ A = \begin{bmatrix} 1 & 3 & 5 & 7 \\ 6 & 0 & 4 & 12 \\ 0 & 3 & 6 & 15 \\ 6 & 0 & 6 & 24 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 1 \\ 4 \\ 9 \\ k \end{bmatrix}. \]
(a) Find the condition on \( k \in \mathbb{R} \) such that \( A\mathbf{x} = \mathbf{b}, \mathbf{x} \in \mathbb{R}^n \) is solvable.
(b) Find all solutions when the condition in (a) holds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89b1189c-c32b-4144-b592-a832138b3e54%2F5a7677a5-5e17-41b0-a9f0-7d8208dfb6c8%2Fgmjtm4_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let
\[ A = \begin{bmatrix} 1 & 3 & 5 & 7 \\ 6 & 0 & 4 & 12 \\ 0 & 3 & 6 & 15 \\ 6 & 0 & 6 & 24 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 1 \\ 4 \\ 9 \\ k \end{bmatrix}. \]
(a) Find the condition on \( k \in \mathbb{R} \) such that \( A\mathbf{x} = \mathbf{b}, \mathbf{x} \in \mathbb{R}^n \) is solvable.
(b) Find all solutions when the condition in (a) holds.
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