Question

Use the Gauss jordan elimination to find the solution to the following system of equations.

-x +y+z = -1
-x +5y-19z = -13
3x-2y-8z= 0

Select the correct choice below and fill in any answer boxes within your choice.

a. there is one solution. the solution is x=__, y=__ and z=___
b. there are infinitely many solutions. if z is any real number, x=__ and y=__.
c. there is no solution.

Answer 1

@jim_thompson5910

Answer 2

-x +y+z = -1
-x +5y-19z = -13
3x-2y-8z= 0


-1 1 1 | -1
-1 5 -19 | -13
3 -2 -8 | 0



1 -1 -1 | 1 -1*R1
-1 5 -19 | -13
3 -2 -8 | 0


1 -1 -1 | 1
0 4 -20 | -12 R2 + 1*R1
3 -2 -8 | 0


1 -1 -1 | 1
0 4 -20 | -12
0 1 -5 | 3 R3 - 3*R1


1 -1 -1 | 1
0 1 -5 | -3 (1/4)*R2
0 1 -5 | 3


1 -1 -1 | 1
0 1 -5 | -3
0 0 0 | 0 R3 - 1*R2


1 0 -6 | -2 R1 + 1*R2
0 1 -5 | -3
0 0 0 | 0


Since the last row is 0 0 0 | 0 which means

0x + 0y + 0z = 0

or just

0 = 0

Answer 3

since 0 = 0 is always true, there are infinitely many solutions

Answer 4

I'll let you fill out the rest

Answer 5

okay so z= 0 and x= -2 and y= -3

Answer 6

@jim_thompson5910 which one should i circle? B.?? if its infintely many solutions and what should i type in the boxes?

Answer 7

1 0 -6 | -2

turns into

x - 6z = -2

so

x = -2 + 6z

see how I got this?

Answer 8

that is your first solution

do the same thing to find y

Answer 9

can u help me find the y i found the x

Answer 10

0 1 -5 | -3

turns into what?

Answer 11

y=-5-3

Answer 12

y - 5z = -3

solve for y

Answer 13

y= -3+5z

Answer 14

yep

Answer 15

so x = -2 + 6z and y = -3 + 5z

Answer 16

z is the free variable

Answer 17

yes cuz its 0 :)

Answer 18

well z can be any number you want it to be

x and y will depend on whatever value of z you pick

Answer 19

oh okay that makes sense!

Answer 20

that adds further confirmation that there are infinitely many solutions

Answer 21

ohh okay thank you! :)

Answer 22

np