[線代] 請問一題線性系統的證明
Let A be an m*n matrix,and let c be a column vector such that
Ax=c has a unique solution.
If m>n,must the system Ax=b be consistent for every choice of b?
Sol:
If m>n,then the final row of H has all zero entries where A~H and H
has row echelon form.
Let en be the final column of the n*n identity matrix.
Reversing the elementary row operations that reduce A to H,
we see that [H│en] ~ [A│b],and the system Ax=b is therefore inconsistemt.
請問一下這題，H 是 m*n的矩陣且m>n，en是n*1的矩陣，那[H│en]最下面那一列
不是會少一個元素嗎? 那這樣這個augmented matix的表示是對的嗎?
有點不太懂怎麼表達我的疑問...
解答它是想找一個無解的情形逆推回去發現能找到一個b與之對應來說明嗎?
還是有其他證明寫法或是能簡單以白話文說明。
真的感激不盡。謝謝。
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