Help! How do I solve this linear equation?
6x-y+z=0
4x+2y-3z=18
x-3y+2z=-15

Question

unklerhaukus · Answer

can you use matrices?

anonymous · Answer

i can. im teaching myself.

unklerhaukus · Answer

$$\left(\begin{array}\6&-1&1\4&2&-3\1&-3&2\end{array}\right)\left(\begin{array}\x\y\z\end{array}\right)=\left(\begin{array}\0\18\-15\end{array}\right)$$

anonymous · Answer

right...now what do i do?

unklerhaukus · Answer

do you know the valid row operations you can apply?

unklerhaukus · Answer

you can multiply any row by a constant 
$$R_n\rightarrow \alpha R_n$$simply multiply each of the 5 terms in the top row by a scalar

anonymous · Answer

You are really confusing me

unklerhaukus · Answer

you can swap an entire row with another
$$R_n\longleftrightarrow R_m$$

unklerhaukus · Answer

maybe matrices isn't a good idea then

unklerhaukus · Answer

the other operation you can do is add or subtract one row from another$$R_n\rightarrow R_n\pm R_m$$

hero · Answer

I know matrices and I know for a fact that @UnkleRhaukus is confusing you

hero · Answer

You can't teach someone something for the first time that way

unklerhaukus · Answer

what is the easy way to solve this

hero · Answer

I'm saying, you can use matrices, but your approach to demonstrating it will most likely confuse

hero · Answer

I'm going to avoid saying "teach" here

unklerhaukus · Answer

add all the equations together what do you get

(6x-y+z)+(4x+2y-3z)+(x-3y+2z)=0+18-15

unklerhaukus · Answer

$$(6x+4x+x)+(-y+2y-3y)+(z-3z+2z)=3$$

unklerhaukus · Answer

ok that dosent work either, i still cant see an simply way to do this

hero · Answer

Drawing button ?

anonymous · Answer

ive figured it out

unklerhaukus · Answer

did you get x=1

hero · Answer

How?

anonymous · Answer

i added

anonymous · Answer

x=1 y=4 and z=-2

hero · Answer

You can't just "add".

unklerhaukus · Answer

thats right, i want to know your steps helpmewithmath2012

hero · Answer

You have to perform a sequence of operations

hero · Answer

I don't think she/he will show them

unklerhaukus · Answer

just outline the method i want to know which rows to add

unklerhaukus · Answer

i want to know your method too hero

anonymous · Answer

i solved y by getting 11x+2y=3 y=4 but idk how i got x and z

unklerhaukus · Answer

did you do it in you head or use paper @helpmewithmath2012 ?

anonymous · Answer

my head so now im trying to figure out what i did

turingtest · Answer

do you know how to find the determinant of a matrix?

zepp · Answer

Can't you simply use row reduction until you get something like|dw:1341437005879:dw|? @UnkleRhaukus