Mathematical Equation Help?

Question

Write the augmented matrix of the system and use the matrix method to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter Z.

2x+y+z=9
-z-y+z= 1
3x-y+z=9

Please help me out on this one...it says the solution is (2,1,4) why am I stuck at

{1 1 -1} 1
{0 -1 3} 9
{0 -4 4} 6

someone please help!

Answer 1

So you went from here:

[2 1 1 | 9]
[-1 -1 1 | 1]
[3 -1 1 | 9]

To here:

[1 1 -1| 1]
[0 -1 3| 9]
[0 -4 4| 6]

Your next step would be to multiply the second row by -1.

[1 1 -1| 1]
[0 1 -3| -9]
[0 -4 4| 6]

Now, surround that 1 you just created on the second row with 0s. This is done by subtracting the first row with the second row, and adding 4 times the second row to the third row.

R1 -> R1 - R2
R3 -> R3 + 4R2

[1 0 2 | 10]
[0 1 -3| -9]
[0 0 -8| -30]

R3 -> -1/8 R3

[1 0 2 | 10]
[0 1 -3| -9]
[0 0 1| 30/8]


I'll let you complete it from here. Basically, make the values above the 1 equal to 0.