Question

If A is an n x n matrix function such that A and \(\frac{dA}{dt}\)are the same function, then A = c\(e^tI_n\)for some constant c.
True or false? why?
Please, help

Answer 1

If \(A=\left(\begin{matrix}e^{t} & 2e^{t} \\ 3e^{t}& 4e^{x}\end{matrix}\right)\), what is \(\frac{dA}{dt}\)?

Answer 2

\[\frac{dA}{dt}=A ~~but~~A\neq ce^tI_n\]therefore, it's false, right?

Answer 3

@MayMay_69