課程名稱︰線性代數
課程性質︰必修
課程教師︰呂學一
開課學院：電機資訊學院
開課系所︰資訊工程學系
考試日期（年月日）︰103/10/7
考試時限（分鐘）：60分鐘
試題 :
台大資工雙班線性代數第一次小考
2014年10月7日下午四點起一個小時
總共四題，每題十分，可按任何順序答題
第一題 Given the definitions of Abelian group and field, you are asked to
describe the definition of vector space (V, F, +,‧).
第二題 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.
第三題 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.)
第四題 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).