Solve the system of given equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.begin{cases}x+3y=0x+y+z=13x-y-z=11end{cases}

Kaycee Roche 2021-02-08 Answered

Solve the system of given equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
{x+3y=0x+y+z=13xyz=11

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Expert Answer

cheekabooy
Answered 2021-02-09 Author has 83 answers

Step 1
Given
{x+3y=0x+y+z=13xyz=11
Step 2
We write the given system of equation in the form
AX=B
where
A=[130111311],B=[xyz] and B=[0111]
The augmented matrix for the given system of the equation can be represented as
[A|B]=[1300111131111]
R2R2R1 and R3R33R1
[A|B]=[13000211010111]
R212R2
[A|B]=[1300011212010111]
R3R3+10R2
[A|B]=[13000112120066]
R316R3
[A|B]=[13000112120011]
Step 3
We write the system of the linear equation as
x+3y=0
y12z=12
z=1
Plug this in the above equation we get
y12(1)=12
y+12=12
y=1212
y=1
Plug this in the above equation
x+3(1)=0
x3=0
x=3
x=3,y=1 and z=1

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Jeffrey Jordon
Answered 2022-01-27 Author has 2047 answers

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