For the following systems of linear equations,
1) x₁ + 2x₂ - 4x₃ = 5
6x₁ + 12x₂ - 18x₃ = 12
2) x₁ + (x₂/2) + (1/4)x₃ = 1/4
x₁ + x₂ + 2x₃= 2
6x₁ + 6x₂ + 2x₃ = -9
3) x₁ + x₂ + 2x₃ = 2
-2x₁ - 2x₂ + x₃ = 2
x₁ + x₂ + 2x₃ = 5
, perform the following tasks:
(i) Put the system into row reduced echelon (canonical) form. Note, pivot points should be the only non-zero number in its column.
(ii) (Row Reduced Echelon Form using MATLAB) Create a variable in MATLAB called aug_matrix that contains the entries of the matrices above. Apply the command rref to aug_matrix and compare the result with (i).