Solve the linear system 2x13x2x31 x1 x30 x12x22x30 x1 x2 x3S

Solve the linear system:

2x₁+3x₂-x₃=1

x₁   +x₃=0

-x₁+2x₂-2x₃=0

[x₁, x₂, x₃]=

Solution

2x1 + 3x2 -x3 =1 -----(1)

x1 + x3 =0 --------(2)

-x1 +2x2 -2x3 =0------(3)

Fom equation 2 : x1 = -x3

So, equation 1 becomes 2x1 +3x2 +x1 =1-----> 3x1 +3x2 =1

So, equation 3 becomes   -x1 +2x2 +2x1 =0-------> x1 +2x2 =0

x1 = -2x2

So, 3( -2x2) +3x2 =1----> -3x2 =1

x2 = -1/3

x1 = 2/3

x3 = -x1 = -2/3

Solution { x1, x2, x3} = { 2/3 -1/3 ,- 2/3}