SOLUTION: 2x₁+3x₂ =-2 x₁+2x₂+3x₃=0 -x₂-5x₃=1 Give the matrix equation associated with the system of equations below, and solve it by usin

Algebra ->  Matrices-and-determiminant -> SOLUTION: 2x₁+3x₂ =-2 x₁+2x₂+3x₃=0 -x₂-5x₃=1 Give the matrix equation associated with the system of equations below, and solve it by usin      Log On


   

Question 950463: 2x₁+3x₂ =-2
x₁+2x₂+3x₃=0
-x₂-5x₃=1

Give the matrix equation associated with the system of equations below, and solve it by using the corresponding inverse mix.
What I've done so far.
2 3 0 [x] =-2
1 2 3 [y] =0
0 1 5 [z] =1
[x]=[2 3 0] ^-1.......[-2 ]
[y]=[1 2 3]............[ 0 ]
[z]=[0 1 5]...........[ 1 ]
I'm not sure if I'm doing it right. Please show me the steps. I'm currently working on it BTW. Thanks.
Found 2 solutions by Fombitz, Newb:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Your third equation is -x%5B2%5D-5x%5B3%5D=1
So the last row of the matrix should be 0 -1 -5.
Ax=b
x=A%5E%28-1%29b
A=%28matrix%283%2C3%2C2%2C3%2C0%2C1%2C2%2C3%2C0%2C-1%2C-5%29%29
A%5E%28-1%29=%28matrix%283%2C3%2C-7%2C15%2C9%2C5%2C-10%2C-6%2C-1%2C2%2C-1%29%29

x=%28matrix%283%2C1%2C23%2C-16%2C3%29%29

Answer by Newb(4) About Me  (Show Source):
You can put this solution on YOUR website!
Fombitz
Good catch for the first.
For the second part I got
Determinant: -14+15-0=1
M11=-7
M12=-15
M13=9
M21=-5
M22=-10
M23=6
M31=-1
M32=-2
M33=1
-7|15|9
5|-10|-6
-1|2|1
I don't understand the last part. Please clarify if you can. Thanks.