Hello

I'm not sure here:

...

Are the following statements true or false? Prove your answer!

1)

The curve is a solution of an initial value problem

2)

Let A be a 2x2 diagonal matrix. The initial value problem

has exactly one solution for each arbitrary

...

1)

Well we call this curve then but is this already enough for being an initial value problem because

so the first two components of aren't a linear combination of any entry of ??? How can I argue here?

2)

Here I think this is true because the solution for in the one-dimensional case is unique according to our lecture. But how to prove this?

What do you think?

Regards