Find the general solution of the system whose augmented matr

Find the general solution of the system whose augmented matrix is (1 1 1 0 4 | | 1 2). The row reduced echelon form is (1 0 0 1 4 -4 2 -1) and so the solution is z = t, y = 4t, x = 2 - 4t.

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 (inversing the sign in the whole row)

Eliminate the 2nd column

Solution set:

x = 2 - 4t

y = -1 + 4t

z = t

	X1	X2	X3	b
1	1	1	0	1
2	1	0	4	2