﻿ 求救！線性代數的方程式有解無解情況討論的問題(頁 1) - 大學的數學 - Math Pro 數學補給站

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### 求救！線性代數的方程式有解無解情況討論的問題

[size=3]以(數字)代表題號，以暗紅色代表題目，以藍色代表自己的理由

[size=3][color=darkred](1)If b屬於C(A) then the linear equation Ax=b is solvable.[A是矩陣，C(A)是A的Column space)[/color][/size]
[size=3][color=darkslateblue][color=blue][自解]對。這是定義[/color]
[/color][color=darkred](3)If one is solving 4 linear non-homogeneous equations involvibg 5 unknowns, there will aways be infinitely many solutions.[/color][/size]
[size=3][color=#8b0000](4)If one is solving 4 linear non-homogeneous equations involvibg 4 unknowns, there will aways have unique solution.[/color][/size]
[size=3][color=#8b0000](6)Four linear homogeneous equations involving 3 unknowns always have solution.[/color][/size]
[size=3][color=#0000ff][自解]錯。有可能無解(只要有至少兩條方程式係數相同)[/color]
[color=#8b0000](5)If one is solving 6 linear non-homogeneous equations involvibg 4 unknowns, usually (means full rank case) there will be many solutions, but occasionally (means not in the case of full rank) there will be one or no solutions.[/color][/size]
[size=3][color=#0000ff][自解]錯。在非full rank的情況下，只可能出現無限多解或無解，不可能有唯一解[/color]
[color=#8b0000](8)The zero solution is always a solution to homogeneous linear equations, and sometimes can be the solution to non-homogeneous linear equations.[/color][/size]
[size=3][color=#8b0000][/color][color=#0000ff][自解]錯。非齊次方程不可能有零解，因為Ax=b,b不為0[/color][/size] [size=3][color=black]今天問老師，要用rref討論可能的情形，所以不能照這樣寫[/color][/size]
[size=3][color=black]那應該怎麼做？[/color][/size]