Solve using GaussJordan elimination 4x1 16x2 39x3 61 2x1

Solve using Gauss-Jordan elimination. 4x_1 + 16x_2 - 39x_3 = 61 2x_1 + 14x_2 - 34x_3 = 58 x_1 + 5x_2 - 12x_3= 20 Select the correct choice below and fill in the answer box(es) within your choice. The unique solution is x_1 = _, x_2 =_, and x_3 = _. The system has infinitely many solutions. The solution is x_1 = _, x_2 =_, and x_3 = t. (Simplify your answers. Type expressions using t as the variable.) The system has infinitely many solutions. The solution is x_1 = _, x_2 = s, and x_3 = t. (Simplify your answer. Type an expression using s and t as the variables.) There is no solution.

Solution

a) is the answer

x1 = -3

x2 = 7

x3 = 1

Solution :

1.

Find the pivot in the 1st column and swap the 3rd and the 1st rows

2.

Eliminate the 1st column

3.

Make the pivot in the 2nd column by dividing the 2nd row by 4

4.

Eliminate the 2nd column

5.

Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)

6.

Eliminate the 3rd column

Solution set:

x1 = -3

x2 = 7

x3 = 1

	X1	X2	X3	b
1	1	5	-12	20
2	2	14	-34	58
3	4	16	-39	61