Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.

Answer 1

3x - 2y + 2z - w = 2
4x + y + z + 6w = 8
-3x + 2y - 2z + w = 5
5x + 3z - 2w = 1

Answer 2

well, this is much more involved and would take a very long time for me to draw it all out. I think it would be easier to see a few examples and a walk-threw

Answer 3

A. (2, 0, 3/37, 9/37)
B. ( 1, -1/3, 4/9, 6)
C. ∅
D. ( 1/2, 0, -37/3, 37/9)

Answer 4

Okay if that will help me!

Answer 5

http://www.math.fsu.edu/~bellenot/class/f08/lalab/other/rref2.pdf

Answer 6

you could plug in each solution to check

Answer 7

so make x = 2,y=0,....

Answer 8

in the long run it is exactly this
elimination method for 2 equations with 2 variables
y+3x=7
2y+2x=7
we multiply the first equation by -2
-2y-6x=-14
2y+2x=7
now we add the equations
-4x=-7
x=7/4

Answer 9

i already tried that and i got nowhere

Answer 10

its the same thing but with n equations and n variables

Answer 11

well if none of the solutions made sense when you pluged them in, then the system has no solutions, and thus we choose c the nullset

Answer 12

well i wanted someone to basically make sure of my answer!!!

Answer 13

@ganeshie8 helpp please :/

Answer 14

wolfram is the best thing to double confirm ur work : it says the same - No soultion exist

http://www.wolframalpha.com/input/?i=Solve+%3A+3x+-+2y+%2B+2z+-+w%09%3D%092%2C++4x+%2B+y+%2B+z+%2B+6w%09%3D%098%2C++-3x+%2B+2y+-+2z+%2B+w%09%3D%095%2C++5x+%2B+3z+-+2w%09%3D%091

Answer 15

But it is good to get hang of gaussian elimination as it is useful when u deal wid finidng inverses and stuff..

Answer 16

oh gosh what would i do without @ganeshie8 (:

Answer 17

for sure
it did not want you to just check the solutions
it wants you to use elimination. you should take the time to learn this
it really is just adding and multiplying easy numbers (lots of them sometimes)
but you will need to know how to do it at some point.

Answer 18

^

Answer 19

hmm that link sucks, ignore it and ill find a better one.

Answer 20

http://linear.ups.edu/jsmath/latest/fcla-jsmath-latestli18.html
this is good. I think you should read it all. you can pm me if you have questions.