- #1
Jamin2112
- 986
- 12
This problem, and all the others on this homework assignment, are making me angry.
Find the general solution of the system of equations.
...
x'=[-3 5/2; -5/2 2]x
Just watch me solve
Assume there's a solution x= $ert, where I'm denoting a vector with constant entries $.
----> (A-rI)=$
----> (A-rI) is singular
----> det(A-rI)=0
---->(-3-r)(2-r)-(-5/2)(5/2)=0
----> r= 1/2
---->(A-(1/2)I)$=(0 0)T
But then I have a problem because the only solution is $=(0 0)T.
I'd know how to proceed, were it not for this dilemma. Next I would Assume there's a second solution x=$tert + #ert, where # is another vector with constant entries, and then solve.
Homework Statement
Find the general solution of the system of equations.
...
x'=[-3 5/2; -5/2 2]x
Homework Equations
Just watch me solve
The Attempt at a Solution
Assume there's a solution x= $ert, where I'm denoting a vector with constant entries $.
----> (A-rI)=$
----> (A-rI) is singular
----> det(A-rI)=0
---->(-3-r)(2-r)-(-5/2)(5/2)=0
----> r= 1/2
---->(A-(1/2)I)$=(0 0)T
But then I have a problem because the only solution is $=(0 0)T.
I'd know how to proceed, were it not for this dilemma. Next I would Assume there's a second solution x=$tert + #ert, where # is another vector with constant entries, and then solve.