True OR False, And Justify Q Assume X = [X₁ X² X3 ] ³ €R³, A- [³ ! ;] there 3 b= (12). Then for Ax=b, x30 basic feasible solutions, are
True OR False, And Justify Q Assume X = [X₁ X² X3 ] ³ €R³, A- [³ ! ;] there 3 b= (12). Then for Ax=b, x30 basic feasible solutions, are
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**True or False Question:**
**Q:** Assume \(\mathbf{x} = [x_1 \ x_2 \ x_3 ]^T \in \mathbb{R}^3\), \(A = \begin{bmatrix} 3 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}\), \( \mathbf{b} = \begin{bmatrix} 12 \\ 10 \end{bmatrix} \). Then for \(A\mathbf{x} = \mathbf{b}\), \(\mathbf{x} \geq 0\) there are 3 basic feasible solutions.
**Explanation of Constants and Matrices:**
- \(\mathbf{x}\) is a vector in \(\mathbb{R}^3\) with elements \(x_1\), \(x_2\), and \(x_3\).
- \(A\) is a \(2 \times 3\) matrix given by \(\begin{bmatrix} 3 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}\).
- \(\mathbf{b}\) is a vector in \(\mathbb{R}^2\) given by \(\begin{bmatrix} 12 \\ 10 \end{bmatrix}\).
**Objective:** Determine if the system \(A\mathbf{x} = \mathbf{b}\) under the condition \(\mathbf{x} \geq 0\) has exactly 3 basic feasible solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e71c6f0-fdac-4001-9095-2485c121cf1d%2F010184dd-69c5-475c-a4fe-cc59e117ca0e%2Fsyx9i9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**True or False Question:**
**Q:** Assume \(\mathbf{x} = [x_1 \ x_2 \ x_3 ]^T \in \mathbb{R}^3\), \(A = \begin{bmatrix} 3 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}\), \( \mathbf{b} = \begin{bmatrix} 12 \\ 10 \end{bmatrix} \). Then for \(A\mathbf{x} = \mathbf{b}\), \(\mathbf{x} \geq 0\) there are 3 basic feasible solutions.
**Explanation of Constants and Matrices:**
- \(\mathbf{x}\) is a vector in \(\mathbb{R}^3\) with elements \(x_1\), \(x_2\), and \(x_3\).
- \(A\) is a \(2 \times 3\) matrix given by \(\begin{bmatrix} 3 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}\).
- \(\mathbf{b}\) is a vector in \(\mathbb{R}^2\) given by \(\begin{bmatrix} 12 \\ 10 \end{bmatrix}\).
**Objective:** Determine if the system \(A\mathbf{x} = \mathbf{b}\) under the condition \(\mathbf{x} \geq 0\) has exactly 3 basic feasible solutions.
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