Determine the general solution for each of the following hom

Determine the general solution for each of the following homogeneous systems. x_1 + 2x_2 + x_3 +2x_4 = 0, 2x + y + z = 0, (a) 2x_1 + 4x_2 + x_3 + 3x_4 = 0, (b) 2x + y + z = 0, 4x + 2y + z = 0 (b) 6x + 3y + z = 0 8x + 4y + z = 0.

Solution

(A)

Your matrix

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

Eliminate the 1st column

Find the pivot in the 3rd column in the 2nd row (inversing the sign in the whole row)

Eliminate the 3rd column

Solution set:

x1 = - 2x2 - x4

x3 = - x4

x2, x4 - free

(B)

Your matrix

Make the pivot in the 1st column by dividing the 1st row by 2

Eliminate the 1st column

Find the pivot in the 3rd column in the 2nd row (inversing the sign in the whole row)

Eliminate the 3rd column

Solution set:

x = - (1/2)y

z = 0

y - free

	X1	X2	X3	X4	b
1	1	2	1	2	0
2	2	4	1	3	0
3	3	6	1	4	0