课程名称︰线性代数一
课程性质︰数学系大一必修
课程教师︰余正道
开课学院：理学院
开课系所︰数学系
考试日期︰2019年09月27日(五)，11:20-11:45
考试时限：25分钟
试题 :
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.