Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20

A. {(8, -7, -2)}
B. {(-8, -7, 9)}
C. ∅
D. {(2, -7, -1)}

Answer 1

@jim_thompson5910

Answer 2

I recommend using the linear algebra toolkit provided in the link below

http://www.math.odu.edu/~bogacki/lat/

Answer 3

that will perform Gaussian elimination and will do so step by step

Answer 4

UM OK

Answer 5

let me know if you need help using it

Answer 6

YEAH I DO..I FORGET THINGS EASILY

Answer 7

ok click the "Enter" link

Answer 8

then click "Row operation calculator"

Answer 9

I DID

Answer 10

pick 3 rows

then 4 columns

Answer 11

OK DONE

Answer 12

now you should see a blank 3x4 matrix

enter the data values in the boxes

Answer 13

ENTER THESE
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20

Answer 14

yes, but you do NOT enter the variables

Answer 15

so in the first row, you would enter

4, -1, 3, 12

one number per box (in the first row)

Answer 16

the other rows are entered in a similar way

Answer 17

OK

Answer 18

SO THE SECOND WOULD BE

Answer 19

1 4 6 -32

Answer 20

yep

Answer 21

one number per box

Answer 22

OK

Answer 23

I SUBMITTED IT

Answer 24

now click on the button that says "Reduced Row Echelon Form"

Answer 25

it's the button on the far right

Answer 26

OK I DID

Answer 27

what you'll get are the full steps if you performed Gaussian elimination

Answer 28

notice on the very last step (the matrix on the right) we have this row 3

0 0 0 1

this implies that

0x + 0y + 0z = 1

which turns into

0 = 1

but that's FALSE, so there are NO solutions and this system is inconsistent

Answer 29

to represent the idea of "no solutions", we refer to the empty set { } or ∅

Answer 30

I UNDERSTAND WHAT YOU ARE SAYING NOW THANK YOU FOR ALL YOUR HELP @jim_thompson5910 ;-)

Answer 31

you're welcome