lateX of linear system to view more clearly
I have find a general solution to this linear system (included a link to lateX pic):
x_1 - 2x_2 + x_3 - 3x_4 = 1
2x_1 - 4x_2 + 4x_3 + 6x_4 + 4x_5 = 6
-2x_1 + 4x_2 - x_3 - 6x_4 + 2x_5 = 0
1x_1 - 2x_2 - 3x_3 + 3x_3 - 8x_5 = -7
But I end up getting :
x_1 - 2x_2 + x_3 + 3x_4 = 1
x_3 + 2x_5 = 2
Rank(Matrix) = 2
Basic Variables = x_1 x_3
Free Variables = x_2 x_4 x_5
I am unfamiliar with a matrix of this size only yielding two viable rows to work with. Should I proceed in setting the free variables equal to arbitrary numbers and solving for x_1 and x_3 to find the general solution? Help is appreciated.