Question

Solve the linear system below by using row reduction

3x+15y+34z=-2

4x+21y+47z=-1

3x+15y+33z=-4

has the solution

x= , y= , z=

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	3	15	34	-2
2	4	21	47	-1
3	3	15	33	-4

Make the pivot in the 1st column by dividing the 1st row by 3

	X1	X2	X3	b
1	1	5	34/3	-2/3
2	4	21	47	-1
3	3	15	33	-4

Eliminate the 1st column

	X1	X2	X3	b
1	1	5	34/3	-2/3
2	0	1	5/3	5/3
3	0	0	-1	-2

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

	X1	X2	X3	b
1	1	5	34/3	-2/3
2	0	1	5/3	5/3
3	0	0	-1	-2

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	3	-9
2	0	1	5/3	5/3
3	0	0	-1	-2

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

	X1	X2	X3	b
1	1	0	3	-9
2	0	1	5/3	5/3
3	0	0	1	2

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	-15
2	0	1	0	-5/3
3	0	0	1	2

Solution set:

x = -15

y = -5/3

z = 2