Solving system of linear equations

[pinki82]

Find/solve following system of linear equations,

3y_1 + 2y_2 +y_4 = 6
5y_1 - 2y_2 +2y_4 = 5
-2y_1 + y_2 - y_4 = -2



WORK DONE :

I am told that the answers are y_1 = 1 and y_2= 1 and y_4 = 1.
But i don't understand how to obtain these values...
I know how to solve 2 linear systerm of equations...but how do i solve
3 linear system of equations like the one above?

 

[mathmike]

try cramers rule. are you familer with this

 

[HallsofIvy]

How in the world did this get into differential equations? I'm going to move it.

There are a variety of ways of solving systems of equations. Cramer's rule, that mathmike mentions, is simple to set up but involves a lot of tedious calculation. I notice that if you add the first and third equations, y_3 is eliminated and if you subtract twice the third equation from the second, y_3 is again eliminated, leaving you with two equations in two unknowns. Find a way of eliminated either y_1 or y_2 from those two and you have just one equation in one unknown that should be easy to solve.

 

[TD]

If you have learned about matrices, you can solve this by using Gaussian elimination which basically comes down to what HallsofIvy illustrated with lineair combinations to eliminate certain unknowns out of one or more equations. With the subtle difference that in this way, you only work with the coefficients in a matrix and not explicitly with the system and all of its unknowns.