課程名稱︰線性代數一
課程性質︰數學系大一必修
課程教師︰余正道
開課學院：理學院
開課系所︰數學系
考試日期︰2019年09月27日(五)，11:20-11:45
考試時限：25分鐘
試題 :
1. Give an example of an infinite dimensional vector space.
You need to justify your answer.
2. Let S={a_ij∈M_n(F): a_ij = a_ji} be the set of n by n symmetric matrices.
Show that S is a subspace of M_n(F) and determine the dimension dim(S).
3. Let W_1, W_2 be the subspaces of V such that the union W_1∪W_2 is also a
subspace. Show that either W_1⊂W_2 or W_2⊂W_1.