Hello can you please help me with this bases and dimension based problems:
Q1) Give three different bases for F2 and for M[2x2] (F).
Q2) Let U and V be distinct vectors of a vector space V. Show that if {u,v} is a basis for V and a and b are nonzero scalars, then both {u+v, au} and {au, bv} are also bases for V.
Thanks a lot for the help!