Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system equations beloW. 3x, + 3x2 + 6x3 = 12 - 6х, - 6х2 - 12х3-24 - 3x2 + 3x3 = 12 3x, + 3x2 + 6x3 = 0 - 6x1 - 6x2 - 12x3 = 0 - 3x2 + 3xg = 0 X1 Describe the solution set, x = X2 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within X3 your choice (Type an integer or fraction for each matrix element.) O A. x= O B. X= X2 O C. X= + X3 O D. X= X2 + X3

Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system equations beloW. 3x, + 3x2 + 6x3 = 12 - 6х, - 6х2 - 12х3-24 - 3x2 + 3x3 = 12 3x, + 3x2 + 6x3 = 0 - 6x1 - 6x2 - 12x3 = 0 - 3x2 + 3xg = 0 X1 Describe the solution set, x = X2 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within X3 your choice (Type an integer or fraction for each matrix element.) O A. x= O B. X= X2 O C. X= + X3 O D. X= X2 + X3

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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**Title: Systems of Linear Equations: A Parametric Vector Form Approach**

**Introduction:**
This educational segment aims to facilitate your understanding of solving systems of linear equations using parametric vector forms. Through a comparison of two systems of equations, we’ll explore their solution sets and provide geometric insights into their characteristics.

**Example Systems:**
We begin with two systems of equations:

**First System of Equations:**

1. $ 3x_1 + 3x_2 + 6x_3 = 12 $
2. $ -6x_1 - 6x_2 - 12x_3 = -24 $
3. $ -3x_2 + 3x_3 = 12 $

**Second System of Equations:**

1. $ 3x_1 + 3x_2 + 6x_3 = 0 $
2. $ -6x_1 - 6x_2 - 12x_3 = 0 $
3. $ -3x_2 + 3x_3 = 0 $

**Objective:**
1. Describe the solutions of the first system of equations in parametric vector form.
2. Provide a geometric comparison with the solution set of the second system of equations.

**Solution Representation:**
To describe the solution set $ \mathbf{x} $ in parametric vector form, we first introduce the vector representation:

\[ \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \]

**Task:**
Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.)

**Options:**
\[
\text{A. } \mathbf{x} = \begin{bmatrix} \text{ } \\ \text{ } \\ \text{ } \end{bmatrix}
\]
\[
\text{B. } \mathbf{x} = \begin{bmatrix} x_2 \\ x_2 \\ \end{bmatrix}
\]
\[
\text{C. } \mathbf{x} = \begin{bmatrix} \text{ } \\ + x_3 \\ \end{bmatrix}
\]
\[
\text{D. } \mathbf{x} = \begin{bmatrix} x_2

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