Can someone please help me with span questions, we did not spend much time on this topic and only did very trivial questions, now i have to do these and i don't have a single idea where to start.
1
If R^n=span{X1,X2,...,Xk},and A is not=0 mxn, show that AXi is not=o for some i.
2
Show that {x^2+2,3x-x^3,4+x+x^3,x} spans P3
3
Let U=span{v1,v2,v3,...,vk} in a vector space V. If w=a1v1+a2v2+a3v3+...+akvk where a2 is not=0, show that U span{v1,w,v3,...,vk}
Thank you