1. ## linear system

hi
i have the following system.
x+2y+3z+4t+5u=6
x+3y+5z+7t+4u=13
x+4y+7z+10t+3u=20
x+2y+4z+6t+8u=13
with Gauss method,i ended up here,
x+2y+3z+4t+5u=6
y+2z+3t-u=7
z+2t+3u=7
i don't know how to work with the parameters $\displaystyle t$ and $\displaystyle u$.
thanks.

2. Originally Posted by Raoh
hi
i have the following system.
x+2y+3z+4t+5u=6
x+3y+5z+7t+4u=13
x+4y+7z+10t+3u=20
x+2y+4z+6t+8u=13
with Gauss method,i ended up here,
x+2y+3z+4t+5u=6
y+2z+3t-u=7
z+2t+3u=7
i don't know how to work with the parameters $\displaystyle t$ and $\displaystyle u$.
thanks.
Use t and u as free parameters and solve for x, y and z in terms of them.

Start with z, from the last equation z=7-2t-3u, now do y and then x.

CB

3. okay,so for every value $\displaystyle u$and $\displaystyle t$,the system has a unique solution,
$\displaystyle x = -1-10u, y= -7 +t + 7u$ and $\displaystyle z = 7 -2t -3u$.
is it okay ?
thanks.

4. Yes, that is what I get.

5. by the way,is my Gauss method correct,did anyone check it

6. I hadn't before but I just did. Yes, that is correct.