EE2030 Assignment # 10
1. Prove or disprove the following statements.
(a) Any n-linear function : Mnn (F) F is a linear transformation.
(b) Any linear transformation : Mnn (F) F is an n-linear function.
(c) If : Mnn (F) F is an alternating n-linear functi
EE2030 Assignment # 7
1. Let A, B Mnn (F) be invertible. Prove that AB is also invertible and (AB)1 = B 1 A1
2. Let V, W be finite-dimensional vector spaces and T : V W be an isomorphism. Let V0 be a subspace
of V . Prove the followings.
(a) T (V0 ) is a
EE2030 Assignment # 9
1. Let W be the subspace of M22 (R) consisting of all symmetric matrices. The set
0 1
1 2
2 1
1 2
1 2
S=
,
,
,
,
1 0
2 3
1 9
2 4
2 1
generates W . Find a subset of S that is a basis for W .
2. Suppose that the augmented matri