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Expert: - 9/3/2010


Question
hello this problem is difficult, thank you for answering expert!

4x1+3x2+2x3-x4=4
5x1+4x2+3x3-x4=4
-2x1-2x2-x3+2x4=-3
11x1+6x2+4x3+x4=11

I think there should be a solution, however; I am doing row reduction almost
ten times now, and the algebra is getting more difficult, something is right?
any help? if you don't want to write it all out, you can even write the steps
you did.  Thank you


Answer

Matrix
Hello Mike,

It is quite a bit to type out the row reductions, but what I obtained is shown in the attached diagram.  In all the attempts
you made, did you get this one?

Anyhow, I gather you understand how to read off the solution, yes?
x1=1-x4
x2=2+3x4
x3=-3-2x4
x4=x4, i.e. x4 is a free variable, thus there are infinitely many
solutions.

Abe

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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