Question

Solve the corresponding homogeneous system of equations using Gaussian elimination and back-substitution

Answer 1

x-2y-3z=2
y-9z=5
-3x+7y=-1

Answer 2

I solved the solution and got x=12 =0 and y=5 but is that what it's asking for?? I thought homogeneous meant that they equal 0

Answer 3

z=0**

Answer 4

you are correct. I think they want you to solve for the system = 0

Answer 5

so I ignore what they are equal to?

Answer 6

yes, you replace 2 5 -1 with 0 0 0

Answer 7

okay perfect thanks that helps a lot!

Answer 8

the solution to the homogenous system can be added to the solution you already found (because you are adding zero)

the complete solution would be
[ 12 5 0 ] + n* homogenous solution
where n is an arbitrary constant

Answer 9

In this example, wouldn't x,y and z equal zero?

Answer 10

~_~

Answer 11

I don't understand ok!!

Answer 12

x-2y-3z=0
y-9z=0
-3x+7y=0


with just the coefficients
1 -2 -3 0
0 1 -9 0
-3 7 0 0

add 3 times the 1st row to the 3rd row

1 -2 -3 0
0 1 -9 0
0 1 -9 0

add -1 times the 2nd row to the 3rd row
1 -2 -3 0
0 1 -9 0
0 0 0 0

if we pick z=1, we can solve for x and y in terms of z

if we continue to reduced row echelon form
add 2 times 2nd row to 1st row
1 0 -21 0
0 1 -9 0
0 0 0 0

we can "read off" the solution vector as [21 9 1]

the solution is z * [ 21 9 1 ]
where z is any number
this is what you should feet if you solved for x and y in terms of z up above