Solving Linear System with Gaussian Elimination - Help for Beginner

[shane1]

I've taken about 3 year break from this style of math, I've been doing Calculus since then. I am taking a beginning linear algebra course and I have a system I have to solve with Gaussian Elimination. I know how to work towards a solution and what Gaussian Elimination is. However when I look at this one I just can not see how to start it up.

Oh yea, the system is:
x + 2y - z = 4
y - z = 3
x + 3y =2z = 7
2u + 4w + x +7y = 7

Also if someone on here would be able to post the code for how to get Latex to display it is an augmented matrix I'd be really greatful.

I feel with this I just need a kick in the right direction.

-Shane

 

[0rthodontist]

Pick a pivot. In this it looks like a good choice is x in the x + 2y - z = 4. Then eliminate all other variables in that position. The other rows containing an x are x + 3y + 2z = 7 and 2u + 4w + x + 7y = 7.

It would be easier to do if you had it in a matrix so that the variables are all in order, from x to z.

 

[fourier jr]

i found this latex code for a matrix:

[tex ]V = \left( \begin{array}{ccc}1-\frac{1}{2}\lambda^2 & \lambda & A\lambda^3(\rho-i\eta) \\-\lambda & 1-\frac{1}{2}\lambda^2 & A\lambda^2 \\A\lambda^3(1-\rho-i\eta) & -A\lambda^2 & 1\end{array} \right)[/tex]

which produces this

$$V = \left( \begin{array}{ccc}1-\frac{1}{2}\lambda^2 & \lambda & A\lambda^3(\rho-i\eta) \\-\lambda & 1-\frac{1}{2}\lambda^2 & A\lambda^2 \\A\lambda^3(1-\rho-i\eta) & -A\lambda^2 & 1\end{array} \right)$$

it's not augmented but i think it still works. it's not necessary to augment your matrices but it might help to remember where the numbers are on one side of the equations. i don't like to augment my matrices because i always forget that there are numbers over there & then i don't do the operations on them.

as orthodentist said, the first thing you've got to do is pick a pivot. i would go with one that has 1 as its coefficient because it saves a lot of work. it's easier to multiply things by multiples of 1 than some other number or a fraction. then you've got to decide what order you want the other variables in. & you've got to make sure all the equations are written with them in the same order. & don't forget that the coefficient of a certain variable is 0 when it doesn't appear in an equation!