Set V = { A MnR |for all i and j, Aij = Aji } (the members of V are precisely the skew-symmetric matrices).

Set V = { A ∈ MnR |for all i and j, Aij = −Aji } (the members of V are precisely the skew-symmetric matrices). Show that V is a vector subspace of MnR, find a basis for V , and determine dim V , the dimension of V .

let a11 a12A a13 ... a 1n a12a 22 a 23... a2n a13a 23a33.. a3n .......... b11 b12B b13 ... b 1n b12b22 b23... b2 n b13b23b33.. b3n .......... a11 a12mA nB m a13 ... a 1n ma11 nb11...