Finding Solution Set for Vectors

[symsane]

How can I determine the solution set?

(1+2i)x₁ + (1-i)x₂ + x₃ = 0,
ix₁ + (1+i)x₂ - ix₃ = 0,
2ix₁ + ix₂ + (1+3i)x₃ = 0.

Thanks..

 

[Defennder]

Simply perform row-reduction to reduce the system to its row echelon form. The only difference with this and matrices containing only real numbers is that you can now multiply row by complex numbers as well.

 

[HallsofIvy]

Or just solve the three equations the way you learned to solve linear equations way back. For example, subtracting 2 times the second equation from the third eliminates x1.