I liked Hirsch and Smale's old book called something like "Linear algebra, differential equations, and dynamical systems". It is now replaced by an expanded edition with a 3rd author added and a longer title, that I expect is also good, though I haven't looked at it.
I don't know if the H&S book is beginner friendly, but what I found good about it was studying linear algebra and differential equations at the same time, i.e. treating them as closely related topics rather than separate ones. So you could use your physical intuition about (say) a harmonic oscillator (mass on a spring, the archetypal second order ODE), then see how the 2nd order equation can be separated into a system of first order ODE's, and solved by finding matrix eigenvalues.
That worked better for me than the abstract linear algebra approach that was purely about vector spaces with nothing going on in them. It showed real sensible motivations of linear algebra.
I don't know if the H&S book is beginner friendly, but what I found good about it was studying linear algebra and differential equations at the same time, i.e. treating them as closely related topics rather than separate ones. So you could use your physical intuition about (say) a harmonic oscillator (mass on a spring, the archetypal second order ODE), then see how the 2nd order equation can be separated into a system of first order ODE's, and solved by finding matrix eigenvalues.
That worked better for me than the abstract linear algebra approach that was purely about vector spaces with nothing going on in them. It showed real sensible motivations of linear algebra.