Question

Using Gaussian elimination and back substitution solve the following system of equation

Answer 1

x-4y-z=-13
-2x+3y+3z=2
3x-5z=17
9x+2y=-1

Answer 2

I have a 4th row... does that mean that it's no solvable

Answer 3

Does that mean I ignore the last part and just find x y and z??

Answer 4

in other words, you have 4 planes that might intersect at a common line or point, right?

Answer 5

what do you mean?

Answer 6

sorry, i assumed you were familiar with the question you posted.

im trying to get a sense of what this system of equations represents is all

Answer 7

rref{{1,-4,-1,13},{-2,3,3,-2},{3,0,-5,-17},{9,2,0,1}}

the wolf made nice work of that for me ....

since the last row is all zeros, and 0 always equals zero, then the common intersection seems to be a plane ...

Answer 8

so I am right in sayingx=-1 y=4 and z=-4

Answer 9

my gut says yes .... but now youve got me wondering

Answer 10

the row of zeros simply means that one of these equations can be written as a multiple of the others

Answer 11

lets test it out :)

Answer 12

x-4y-z=-13
-1 4 -4
-------
-1-16+4 = -13


-2x+3y+3z=2
-1 4 -4
-----------
2 +12 -12 = 2


3x-5z=17
-1 -4
------
-3+20 = 17


9x+2y=-1
-1 4
-------
-9+8 = -1


they fit

Answer 13

Ahhhh good! I was just caught a little off guard by the fourth row haha thank you!!

Answer 14

i agree that was a little off putting :) but as long as the last row didnt end in a nonzero value, were good