Then prove ha therefore w is a subspace of v(f). example: f m,(f) is a vector space of all 2 x 2 matrices over the f1eld a b -b a over f will be a subspace of m

then prove ha Therefore W is a subspace of V(F). Example: f M,(F) is a vector space of all 2 x 2 matrices over the f1eld a b -b a over F will be a subspace of M.(F). set W of all matrices of the form Solution. Let a = D W. D Wand peFthen b a a, g+8- a b, a, b, , t b, +b, a+-b a-b, a,b, ba,+a a,+@ W (, +b,) a, ta,) a, b, pa pb and po Pb, a,) P-b,) pa, pa pb,e W (pb,) pa, W Therefore W is closed for the vector addition and scalar multiplic Hence M(F) is a subspace. Example: if a, a ,if we take p as -2 than the form of matrix will change than how it becomes a subspace of v