Describe the solutions of the first system of equations below in parametric vector form. Provide a geometriccomparison with the solution set of the second system of equations below.4x₁ +4x2 + 8x3 = 16- 12x₁-12x₂-24x3 = - 48- 6x₂ + 12x3 = 12X₁Describe the solution set, x= x₂4X34x₁ + 4x2 + 8x3 = 0- 12x₁-12x₂ - 24x3 = 0- 6x₂ + 12x3 = 0of the first system of equations in parametric vector form. Select the correctchoice below and fill in the answer box(es) within your choice.(Type an integer or fraction for each matrix element.)

Given the system of equationsLet us use Gaussian elimination to calculate the solution to the…

Answered: Describe the solutions of the first…

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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Related questions

Question

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.
4x₁ +4x2 + 8x3 = 16
- 12x₁-12x₂-24x3 = - 48
- 6x₂ + 12x3 = 12
X₁
Describe the solution set, x= x₂
4
X3
4x₁ + 4x2 + 8x3 = 0
- 12x₁-12x₂ - 24x3 = 0
- 6x₂ + 12x3 = 0
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.
(Type an integer or fraction for each matrix element.)

Expert Solution

Step 1: Writing down the augmented matrix

Given the system of equations

$table row cell 4 x subscript 1 plus 4 x subscript 2 plus 8 x subscript 3 end cell equals 16 row cell negative 12 x subscript 1 minus 12 x subscript 2 minus 24 x subscript 3 end cell equals cell negative 48 end cell row cell negative 6 x subscript 2 plus 12 x subscript 3 end cell equals 12 end table$

Let us use Gaussian elimination to calculate the solution to the system.

The augmented matrix is

$open square brackets right enclose table row 4 4 8 row cell negative 12 end cell cell negative 12 end cell cell negative 24 end cell row 0 cell negative 6 end cell 12 end table end enclose table row 16 row cell negative 48 end cell row 12 end table close square brackets$