Find the solutions of the following system by reducing it to

Find the solution(s) of the following system by reducing it to the reduced row echelon form. Write down each row operation performed to the augmented matrix. (6) x_1, + x_2 - x_3 = 6 -2x_1 - x_2 + x_3 = 6 -x_1 - 2x_2 + x_3 = 2

Solution

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

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

Eliminate the 3rd column

Solution set:

x1 = -12

x2 = -8

x3 = -26

	X1	X2	X3	b
1	1	1	-1	6
2	-2	-1	1	6
3	-1	-2	1	2