hayharbr!! i have another question since you seem to understand this..?! or anyone else?

Question

I got stuck on this the question is....

use row operations to solve the system.
x - y = 4
y - z = -3
x + z = 5

i got all the way to getting
x-y=4, y-z=-3 and z=2 an
d they said the final answer is {(3, -1, 2)}
how did they get from 4,3,2 to 3,-1,2?

thank you vincent g!

Answer 1

You have z=2, and y-z=-3, so if you put the value of z in there you should have
y - 2 = -3
so y is -1
Now, with the value of y, you can replace it in the x-y=4 equation
x-(-1)=4
so x=3

You were on the right track, you just stopped a bit short of the finish line.

Answer 2

Set up your initial rows:

1 -1 0 4
0 1 -1 -3
1 0 1 5

Then start multiplying and combining until you have the matrix:

1 0 0 x
0 1 0 y
0 0 1 z

and these will be your answers.

(Add row 2 to row 1)
1 0 -1 1
0 1 -1 -3
1 0 1 5

(Add row 3 to row 1)
2 0 0 6
0 1 -1 -3
1 0 1 5

(Divide row 1 by 2)
1 0 0 3
0 1 -1 -3
1 0 1 5

(Add Row 2 to row 3)
1 0 0 3
0 1 -1 -3
1 1 0 2

(Add negative row 1 to row 3)
1 0 0 3
0 1 -1 -3
0 1 0 -1

(Swap rows 2 and 3)
1 0 0 3
0 1 0 -1
0 1 -1 -3

(Multiply row 3 by -1)
1 0 0 3
0 1 0 -1
0 -1 1 3

(Add row 2 to row 3)
1 0 0 3
0 1 0 -1
0 0 1 2

x = 3, y = -1, z = 2

Answer 3

If you've gotten to z=2, then putting z into your second equation lets you determine that y=-1. You can also substitute z=2 in th third equation and you'll find that x=3.

Answer 4

you got Z = 2 ...
now back substitute .... if z = 2 ... the [eq2] y - 2 = -3 ... y=-1

if y = -1 ... [eq1] x - (-1) = 4 .... x = 5

Answer 5

Why can't all you people do your own FCUKING HOMEWORK

Answer 6

DO YOUR OWN FUGGIN HOMEWORK