Question

use the echelon method to solve the following system of three equations
5x-2y+5z=59
3x-2y-3z=-1
x-y+2z=12

Answer 1

Hey sorry for not responding sooner (it takes me a while to do these).
Anyway I would first set up the matrix like so:
[5 -2 5|59]
[3 -2 -3|-1]
[1 -1 2|12]
If you swap the first with the third row you have this:
[1 -1 2|12]
[3 -2 -3|-1]
[5 -2 5|59]
Next let your new Row2=row2-3*(row1) and let your new Row 3 = row3-5*(row1). Then you will have:
[1 -1 2|12]
[0 1 -9|-37]
[0 3 -5|-1]
Next make your new Row3=row3-3*(row2). Then you should have:
[1 -1 2|12]
[0 1 -9|-37]
[0 0 22|110]
Then for your new Row3 multiply 1/22 with your old row3. So you have:
[1 -1 2|12]
[0 1 -9|-37]
[0 0 1| 5]
Now you have enough information to solve the system of equations.
z=5
y-9z=-37
x-y+2z=12
I leave it to you to finish. :D
Did that help?