Use Gaussian Elimination algorithm to solve the following sy

Use Gaussian Elimination algorithm to solve the following system of linear equations, x + y+ z = 4 2x + 2y + z = 6 x + y + 2z = 6 x + y+ z = 4 2x + 2y + 2 = 4 x + y + 2z = 6 2x_1 + x_2 - x_3 + x_4 - 3x_5 = 7 x_1 + 2x_3 - x_4 + x_5 = 2 -2x_2 - x_3 + x_4 - x_5 = -5 3x_1 + x_2 - 4x_3 - 5x_5 = 6 x_1 - x_2 - x_3 - x_4 + x_5 = 3

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:

x = 2 - y

z = 2

y - free

(b)

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:

The system is inconsistent

(c)

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Eliminate the 1st column

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

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by -11

Eliminate the 3rd column

Make the pivot in the 4th column by dividing the 4th row by -35/11

Eliminate the 4th column

Make the pivot in the 5th column by dividing the 5th row by 59/35

Eliminate the 5th column

Solution set:

x1 = 272/59

x2 = 184/59

x3 = -81/59

x4 = 186/59

x5 = 194/59

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