[理工] [線代]-矩陣與線性方程式 consistent
Find the condition for which the following system is consistent
{2x-y+3z=a
{3x+y-5z=b
{-5x-5y+21z=c
解：
┌ 2 -1 3 │a ┐ ┌2 -1 3 │a ┐
│ 3 1 -5 │b │ r │0 5/2 -19/2 │b-(3a/2) │
└ -5 -5 21 │c ┘ ~ └0 0 0 │c+3b-2a ┘
所以當c+3b-2a=0時，該system為consistent
n*1
補充：若存在Xo∈F 使得AXo=b，稱Ax=b有解或Ax=b為consistent
問題一：
想請問為什麼c+3b-2a=0時為consistent，來回看了好幾次感覺還是卡卡的。
問題二：
如果以補充的定義來看，不曉得在這邊的Xo取一個的話該如何取。
感謝各位耐心看完問題，謝謝。
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