Find the basic solutions and write the general solution as a linear combination of the basic solutions.

x+2y-z+2s+t=0

x+2y+2z+t=0

2x+4y-2z+3s+t=0

Thanks alot.

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- January 6th 2011, 06:24 PMseitSystem of linear equations
Find the basic solutions and write the general solution as a linear combination of the basic solutions.

x+2y-z+2s+t=0

x+2y+2z+t=0

2x+4y-2z+3s+t=0

Thanks alot. - January 6th 2011, 06:26 PMpickslides
What methods have you been taught or are you allowed to use?

- January 6th 2011, 06:53 PMDrSteve
Looks like you're going to want to use some form of Gauss-Jordan Reduction. Why don't you try to start it off so we can see where you get stuck.

- January 7th 2011, 06:21 PMHallsofIvy
You don't really need to use anything as sophisticated as "Gauss-Jordan". For example, subtracting the first two equations immediately eliminates x and y and subtracting twice the second equation from the third does the same thing, leaving two equations to be solved for z, s, and t.

- January 7th 2011, 07:09 PMdwsmith