1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix with complex numbers, linear algebra

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data

    The system of equations:

    ix - y + 2z = 7
    2x + αz = 9
    -x + 2y + 5iz = β

    has a unique solution, except for one value of α. What is this α - value? If the matrix doesn't have a unique solution, then what value should β have for the matrix to be consistent and what is the solution then? (Parameters α, β and the unknowns x, y ,z are complex numbers)

    2. Relevant equations

    3. The attempt at a solution

    I have tried to solve this as a matrix with the echelon form, but I can't get anywhere since I have never before done matrices with complex numbers.
  2. jcsd
  3. Sep 30, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Except for the "difficulty" of remembering that i2= -1, there is no difference. A matrix equation has a unique solution if and only if the determinant of the matrix is non-zero, which is the same as its echelon form having no zeros on the diagonal. If there is a 0 on the diagonal, there are no solutions if the other numbers in that row are non-zero, infinitely many if the other numbers are zero.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Matrix with complex numbers, linear algebra