Question

Solve the system of equations
12 10x1 + x2 + x3 =
12 10 x1 + x2 + x3 =
12 10 x1 + x2 + x3 =
using Gauss-Jordon method with pivoting.

Answer 1

Answer on Question #46675 – Math – Linear Algebra

Question:

Solve the system of equations using Gauss-Jordan method with pivoting.

$$10x_1 + x_2 + x_3 = 12$$ $$10x_1 + x_2 + x_3 = 12$$ $$10x_1 + x_2 + x_3 = 12$$

Solution:

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)

$$\left( \begin{array}{ccccc} 10 & 1 & 1 & 12 \\ 10 & 1 & 1 & 12 \\ 10 & 1 & 1 & 12 \end{array} \right)$$

divide the 1-th row by 10

$$\left( \begin{array}{ccccc} 1 & 0.1 & 0.1 & 1.2 \\ 10 & 1 & 1 & 12 \\ 10 & 1 & 1 & 12 \end{array} \right)$$

from 2; 3 rows we subtract the 1-th row, multiplied respectively by 10; 10

$$\left( \begin{array}{ccccc} 1 & 0.1 & 0.1 & 1.2 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right)$$

Answer: $x_1 + (0.1)x_2 + (0.1)x_3 = 1.2$

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