considered the following equations:

x - 3y + z = 4

2x - 8y + 8z = -2

-6x + 3y - 15z = 9

We can convert the equations into an augmented matrix:

(1)When we look at the start of the left column, we find 1 which is a non-zero number, which means that this works as a pivot.

Next we try to get entry (2,1) to equal zero. To do this we can take one-third times the 3rd row and add it to the 2nd row. (1/3)R3+ R2 = R2. (*we could have also done -2R1+R2=R2)

Now our matrix is:

(2)Now we can try to get a zero in entry (3,1). We can do (6)R1+R3 = R3

Now our matrix is:

(3)Now we can try to get a zero in entry (3,2). We can do (-15/7)R2+R3 = R3

Now our matrix is:

(4)From this we can figure out that z = -2 as the third row means 0x + 0y + (-108/7)z = 216/7.

Now we can substitute Z back into the 2nd equation.

0x + -7y + 3(-2) = 1

y = -1

And finally we can substitute y and z into the 1st equation

1x + -3(-1) + 1(-2) = 4

x = 3

so we have

x = 3

y = -1

z = -2