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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 of equations below. 3x, +3x2 + 6x3 = 12 - 9x, - 9x2 - 18x3 = - 36 - 5x2 + 15x3 = 10 3x, + 3x2 + 6x3 = 0 - 9x, - 9x2 - 18x3 = 0 - 5x2 + 15x3 = 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 your choice. X3 (Type an integer or fraction for each matrix element.) O A. X= Ô B. X=X, O C. X= + X3 O D. x=X2

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 of equations below. 3x, +3x2 + 6x3 = 12 - 9x, - 9x2 - 18x3 = - 36 - 5x2 + 15x3 = 10 3x, + 3x2 + 6x3 = 0 - 9x, - 9x2 - 18x3 = 0 - 5x2 + 15x3 = 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 your choice. X3 (Type an integer or fraction for each matrix element.) O A. X= Ô B. X=X, O C. X= + X3 O D. x=X2

Advanced Engineering Mathematics
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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### Example Problem 1.5.17 Suppose the solution set of a certain system of linear equations can be described as \( x_1 = 5 + 4x_3 \), \( x_2 = -6 - 7x_3 \), with \( x_3 \) free. Use vectors to describe this set as a line in \( \mathbb{R}^3 \). Geometrically, the solution set is a line through \(\_\) parallel to \(\_\).
Transcribed Image Text:### Example Problem 1.5.17 Suppose the solution set of a certain system of linear equations can be described as \( x_1 = 5 + 4x_3 \), \( x_2 = -6 - 7x_3 \), with \( x_3 \) free. Use vectors to describe this set as a line in \( \mathbb{R}^3 \). Geometrically, the solution set is a line through \(\_\) parallel to \(\_\).
### Problem 1.5.19 **Instructions:** 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 of equations. **Systems of Equations:** First System: \[ 3x_1 + 3x_2 + 6x_3 = 12 \\ -9x_1 - 9x_2 - 18x_3 = -36 \\ -5x_2 + 15x_3 = 10 \] Second System: \[ 3x_1 + 3x_2 + 6x_3 = 0 \\ -9x_1 - 9x_2 - 18x_3 = 0 \\ -5x_2 + 15x_3 = 0 \] **Task:** Describe the solution set, \( \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \), of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. **Options:** - **A.** \( \mathbf{x} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **B.** \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **C.** \( \mathbf{x} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} + x_3 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **D.** \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} + x_3 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) (*Type an integer or fraction for each matrix element.*) **Selected Option:** - B. \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \
Transcribed Image Text:### Problem 1.5.19 **Instructions:** 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 of equations. **Systems of Equations:** First System: \[ 3x_1 + 3x_2 + 6x_3 = 12 \\ -9x_1 - 9x_2 - 18x_3 = -36 \\ -5x_2 + 15x_3 = 10 \] Second System: \[ 3x_1 + 3x_2 + 6x_3 = 0 \\ -9x_1 - 9x_2 - 18x_3 = 0 \\ -5x_2 + 15x_3 = 0 \] **Task:** Describe the solution set, \( \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \), of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. **Options:** - **A.** \( \mathbf{x} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **B.** \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **C.** \( \mathbf{x} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} + x_3 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) - **D.** \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} + x_3 \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix} \) (*Type an integer or fraction for each matrix element.*) **Selected Option:** - B. \( \mathbf{x} = x_2 \begin{bmatrix} \_\_ \\ \
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