Determine the unique solution to the linear system

Question

-2x₁ + 2x₂ - 2x₃ + x₄ = -6

        -   x₂ + 2x₃ + x₄  = 0

                3x₃-x₄=7

                      2x₄=4

Answer 1

We need to find the value of all the 4 unique x values.

 

From the last equation, we see that      x₄ = 2

 

Plug in this x value into the 3rd equation to obtain

 

x₃ = 3

 

 

Plug in these known values into the first 2 equations to get

 

-2(x₁ - x₂ + x₃) = -8

x₁ - x₂ + 3 = 4

x₁ - x₂ = 1

 

-x₂ + 2(3) = -2

-x₂ = -8

x₂ = 8

 

Then you can plug in this value of x₂ to find x₁.