System of linear differential equations – complex?
Hello dear community, I know how to solve systems of the form y'=Ay+b with a real-valued nxn matrix A and a real-valued vector b. We had this formula for it. There Y(t) is a principal fundamental matrix. Now, however, complex numbers are allowed for A and b. What does that change? How do I find…
Logical equivalence?
This is about the second part of the problem. How do I find out whether it depends on a or b? My result for the first part is that A is not equivalent to what's written there.
What is that?
-z^(1) *z^(-2) ? So what do you get -z ^ -1 ??? Is that right
why larger/smaller with antisymmetry?
When it comes to antisymmetry of relations, why don't we simply say "If A = B and B = A," then they are the same element, and how is that different from reflexivity? And if A < B and B < A are sufficient to assert antisymmetry, then what is equality in mathematics anyway?
Power set?
M = {1} P(M) = {empty set, 1} Why do we explicitly write the empty set in the power set, but in M = {1} you leave it out, or it is there, but you don't write it down.
Compound interest?
I don't understand B) So for A) I used the formula for compound interest K0= 100,000 i=4.5% = 0.045 n= 5 years I used that and got €124,618 for A) annual interest in arrears, but what about B) if it's monthly? What did I use?
What does " => " mean in mathematics in proofs?
The task is as follows: Verify the truth of the statement by means of direct proof: |z| = 1 => z^n / (1 + z^2n) ∈ IR , z ∈ C How should the arrow be interpreted, and what does it mean for the proof? It's an equation on one side and a term on…