Eigenvalues of coefficient matrix problem

[DrunkApple]

Homework Statement

Determine the general solution of the system of homogeneous differential equations.
The system of homogeneous differential equations is:
X'_{1}(t) = 141x_{1}(t) - 44x_{2}(t)
X'_{2}(t) = 468x_{1}(t) - 146_{2}(t)

What is Eigenvalues of Coefficient Matrix?
What is corresponding eigenvectors?
What is expression for x_{1}(t)?
What is expression for x_{2}(t)

Homework Equations

The Attempt at a Solution

What is Eigenvalues of Coefficient Matrix?
|144 - 44 | = A
|146 -146|
det|144-λ -44 | = P(λ)
|468 -146-λ|
= (144-λ)(-146-λ) - (-44)(468)
= -21024 -144λ +146λ + λ^{2} + 20592
= λ^{2} +2λ -432
Do I use quadratic equation to find λ?

 

[sunjin09]

yes of course, then you find the eigenvectors, then you find your solution to the DE using these eigenvectors