[線代] linear transformation (onto)

看板Math作者 (無法顯示)時間13年前 (2011/05/14 22:22), 編輯推噓2(2推 0噓 3→)
留言5則, 4人參與, 最新討論串1/2 (看更多)
a linear transformation L: V -> W is said to map V onto W if L(V)=W show that the linear transformation L defined by L(x) = ( x1, x1+x2, x1+x2+x3 )^T maps R^3 onto R^3 請問這題要怎麼證呢? 謝謝!! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.28.136
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05/14 22:30, , 1F
你就證明R^3所有向量都能寫成某組(x1,x2,x3)被L的解
05/14 22:30, 1F
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05/14 22:44, , 2F
更明確的說你只要證明 L(x)=[1,0,0], L(x)=[0,1,0]
05/14 22:44, 2F
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05/14 22:45, , 3F
L(x)=[0,0,1] 都有解
05/14 22:45, 3F
推
05/15 03:38, , 4F
Dimension Thm
05/15 03:38, 4F
推
05/15 19:47, , 5F
check injective, this is Linear algebra
05/15 19:47, 5F
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文章代碼(AID): #1Dpf0m1N (Math)