Question

Hello Guys,

my best wished to you all. I just need a new account and this is my first question. Here it goes.

QS: Find fundamental system and general solution of differential equation defined by ..

|1/t t^2 0|
|0 -2/t^2 1/t^2|
|0 0 1/t |

Now, as per my knowledge there are two appropriate approaches into solving this ...

1) state space method
2) solving from downward to above, first finding x3 then x2 then x1.

However, I am not getting the same answer by both mehtod...

MY solution is

Answer 1

r = 1/t, r=1/t, r=-2/t are the eigen values

for r = 1/t, first eigen vector is [1 0 0]'

for r = 1/t, the second eigen vector is [1 1/t^2 3/t]'

for r=-2/t, the eigen vector is [1 -3/t^3 0]

oh, this is really not easy typing it all :(