SOLUTION: x-z=-3 y+z=9 x+z=7 solve the following linear system by using gaussian reduction method matrix

Algebra ->  Linear-equations -> SOLUTION: x-z=-3 y+z=9 x+z=7 solve the following linear system by using gaussian reduction method matrix      Log On


   

Question 1090279: x-z=-3
y+z=9
x+z=7
solve the following linear system by using gaussian reduction method matrix
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

The matrix for the given equations is

matrix%283%2C4%2C1%2C0%2C-1%2C-3%2C0%2C1%2C1%2C9%2C1%2C0%2C1%2C7%29

We first want to get "1 0 0" in column 1. It is already nearly the way we want it; we just need to get a 0 in row 3. To do that, we can replace row 3 with (row 3 - row 1).
R3 <-- R3-R1: 1-1=0; 0-0=0; 1-(-1)=2; 7-(-3)=10:

matrix%283%2C4%2C1%2C0%2C-1%2C-3%2C0%2C1%2C1%2C9%2C0%2C0%2C2%2C10%29

Next we can make smaller numbers in the matrix by dividing row 3 by 2:

matrix%283%2C4%2C1%2C0%2C-1%2C-3%2C0%2C1%2C1%2C9%2C0%2C0%2C1%2C5%29

After this, the second column is already the way we want it. So now we use row 3 to get "0 0 1" in column 3.
R1 <-- R1+R3: 1+0=1; 0+0=0; 1+(-1)=0; -3+5=2
R2 <-- R2-R3: 0-0=0; 1-0=1; 1-1=0; 9-5=4

matrix%283%2C4%2C1%2C0%2C0%2C2%2C0%2C1%2C0%2C4%2C0%2C0%2C1%2C5%29


The solution to the system of equations is x=2, y=4, z=5.