Solve using Gauss-Jordan elimination. X1 - X2 + 3x3 + 3x4 = - 1.1 - 4x, + 6x2 - 7x3 - 22x4 = 14.3 3x, - X2 + 12x3 + 4x, - 3x2 + 8x3+ 15x4 = - 8.3 %3D X4 = 4.2 Select the correct choice below and fill in the answer box(es) within your choice. The unique solution is x, =| O A. (Simplify your answers.) and x4 The system has infinitely many solutions. The solution is x, = , X2 = X3 = and x4 =t. О в. (Simplify your answers. Type expressions using t as the variable.) The system has infinitely many solutions. The solution is x, =, x2 = OC. (Simplify your answers. Type expressions using s and t as the variables.) X3 = s, and x4 = t. O D. There is no solution.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Solve using Gauss-Jordan elimination.**

The system of equations is:

1. \( x_1 - x_2 + 3x_3 + 3x_4 = -1.1 \)

2. \(-4x_1 + 6x_2 - 7x_3 - 22x_4 = 14.3 \)

3. \( 3x_1 - x_2 + 12x_3 + x_4 = 4.2 \)

4. \( 4x_1 - 3x_2 + 8x_3 + 15x_4 = -8.3 \)

**Select the correct choice below and fill in the answer box(es) within your choice.**

- **A.** The unique solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = \_\_\_, \) and \( x_4 = \_\_\_. \)
  
  *(Simplify your answers.)*

- **B.** The system has infinitely many solutions. The solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = \_\_\_, \) and \( x_4 = t. \)
  
  *(Simplify your answers. Type expressions using \( t \) as the variable.)*

- **C.** The system has infinitely many solutions. The solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = s, \) and \( x_4 = t. \)
  
  *(Simplify your answers. Type expressions using \( s \) and \( t \) as the variables.)*

- **D.** There is no solution.
Transcribed Image Text:**Solve using Gauss-Jordan elimination.** The system of equations is: 1. \( x_1 - x_2 + 3x_3 + 3x_4 = -1.1 \) 2. \(-4x_1 + 6x_2 - 7x_3 - 22x_4 = 14.3 \) 3. \( 3x_1 - x_2 + 12x_3 + x_4 = 4.2 \) 4. \( 4x_1 - 3x_2 + 8x_3 + 15x_4 = -8.3 \) **Select the correct choice below and fill in the answer box(es) within your choice.** - **A.** The unique solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = \_\_\_, \) and \( x_4 = \_\_\_. \) *(Simplify your answers.)* - **B.** The system has infinitely many solutions. The solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = \_\_\_, \) and \( x_4 = t. \) *(Simplify your answers. Type expressions using \( t \) as the variable.)* - **C.** The system has infinitely many solutions. The solution is \( x_1 = \_\_\_, \, x_2 = \_\_\_, \, x_3 = s, \) and \( x_4 = t. \) *(Simplify your answers. Type expressions using \( s \) and \( t \) as the variables.)* - **D.** There is no solution.
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