Posted by Michael on Friday, December 4, 2009 at 9:03pm.
(-3-i)x1 + (1-2i)x2 = 0.....(1)
(-7-9i)x1 + (7-4i)x2 = 0 ....(2)
or
Ax=0
The system is a homogeneous equation. A trivial solution is x1=0 and x2=0.
For the system to have non-trivial solutions, the determinant of A must vanish, or |A|=0.
Calculate
|A|
=(-3-i)(7-4i) - (-7-9i)(1-2i)
= -21-4+5i - (-25+5i)
=0
So non-trivial solutions exist, because the two equations are linearly dependent.
Prove that the two equations are linearly dependent by applying Gauss elimination which results in two identical equations. Eliminate the second equation.
Take equation (1),
(-3-i)x1 + (1-2i)x2 = 0
We multiply by the conjugate of (1-2i) to get
(1+2i)(-3-i)x1 + (1+2i)(1-2i)x2 = 0
-(1+7i)x1 + 5x2 = 0
Let x1=5t, where t is a variable parameter, then
-(1+7i)5t + 5x2 = 0
Solving, x2=1+7i
Therefore
x1=5t, x2=1+7i
Make your pick for the answer.
Thanks a lot!
You're welcome!
Related Questions
college - Which of the following choices is a solution for: (-3-i)x1 + (1-2i)x2...
Calculus (Urgent!!) - Hello everyone, I need help with the following problems. ...
Math - Which of the following are linear equations in x1, x2 and x3? (a) x1 + ...
Reply to grant about a regression problem - This is a reply to the question ...
math - I Wanted To Find The Square Root Of (1-2i) But I Didn't Know How To ...
intro to probability - In a study of particulate pollution in air samples over a...
Calculus - Find the partial derivative y with respect to s for the following ...
Linear Algebra - Express the solutions of the following systems in terms of the ...
Operations research - 36) Consider the following minimization problem: Min z = ...
algebra2 - solve the equation: First: x + 3y = 5 Second: 3x - y = 5 should i use...
For Further Reading
