# 求救！線性代數的方程式有解無解情況討論的問題

## 求救！線性代數的方程式有解無解情況討論的問題

(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)
[自解]對。這是定義
(3)If one is solving 4 linear non-homogeneous equations involvibg 5 unknowns, there will aways be infinitely many solutions.

(4)If one is solving 4 linear non-homogeneous equations involvibg 4 unknowns, there will aways have unique solution.
(6)Four linear homogeneous equations involving 3 unknowns always have solution.
[自解]錯。有可能無解(只要有至少兩條方程式係數相同)
(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.

[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
(8)The zero solution is always a solution to homogeneous linear equations, and sometimes can be the solution to non-homogeneous linear equations.

[自解]錯。非齊次方程不可能有零解，因為Ax=b,b不為0

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