课程名称︰线性代数
课程性质︰必修
课程教师︰吕学一
开课学院：电机资讯学院
开课系所︰资讯工程学系
考试日期（年月日）︰103/10/7
考试时限（分钟）：60分钟
试题 :
台大资工双班线性代数第一次小考
2014年10月7日下午四点起一个小时
总共四题，每题十分，可按任何顺序答题
第一题 Given the definitions of Abelian group and field, you are asked to
describe the definition of vector space (V, F, +,‧).
第二题 Prove that in any vector space (V, F, +,‧), we have
0_Fx = a0_V = 0_V
for any scalar a∈F and any vector x∈V.
第三题 Let U and V be two subspaces of vector space W = (W, F, +,‧). Prove
that U +V is a subspace of W such that any subspace ofW containing U∪V has to
contain U + V. (This is our 和子定理.)
第四题 Let R and S be two subspaces of vector space W = (W, F, +,‧).
Given our 罩咖定理 and 和子定理, you are asked to prove
span(R∪S) ⊆ span(R) + span(S).