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