Question

how do i solve the following set of equations?

-x+2y+z+w=0
x+y-z+w=0
-x+y+z=0

Answer 1

There are several ways to do it. Usually, they make you do it the hard way first, then show you the easy ways later.

Answer 2

1. Elimination
2. Substitution
3. Matrices (Gaussian Elimination)
4. Cramer's Rule

Answer 3

what class is this for?

Answer 4

Oh wait, I just noticed all of them equal zero

Answer 5

i tried using matrices but it seems impossible to get the variable values since i have 3 equations but 4 unknowns

Answer 6

For that, there's this:

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

Answer 7

you will have a free variable?

Answer 8

what is free variable?

Answer 9

x = z
y=0
w=0

Answer 10

A free variable is basically what you get since w = 0 as implied by the third row

Answer 11

is this for linear algebra?

Answer 12

so i row reduced and found x = w ,y = 0 and z = 0, but im not sure if this is what you guys are doing in class.

Answer 13

@zzr0ck3r ,yes it is linear algebra

Answer 14

so when you row reduce you get
1 0 -1 0 0
0 1 0 0 0
0 0 0 1 0
right?

Answer 15

from my augmented matrix i get
w=0
y=0
x-y=0 which means x=0

Answer 16

@zzr0ck3r, yes i get that

Answer 17

so first row
x y z w
1 0 -1 0 0
so
x 0 -z 0 0
so x = z

Answer 18

actually it's x-z=0
not x-y=0

Answer 19

yes

Answer 20

so x = z

Answer 21

so like you said x = z, y = 0, w = 0

Answer 22

in other words, there are infinite many solutions.

Answer 23

thanks a lot.@Hero
and @zzr0ck3r

Answer 24

np

Answer 25

thanks @Hero