• find a basis for span(₀^-2 ₀¹),(₃⁰ ₁⁰ ),(₀¹ _-1⁰ ),(₀⁰ ₀¹),(₁⁰ ₀⁰ ) (those are2*2 matrix)
• findabasisfor{fspan(e^x,e^2x,e^3x)|f(0)=f^'(0)=0}
• findabasisfor{fspan(e^x,e^-x,cos(x),sin(x),1,x)|f(0)=f^'(0)=0}

I know the normal way to find some easy basis however, i don't know how to find basis for this kind of equation, could you please tell me how to solve questions like these? like how should I think. thank you :)