線性代數矩陣證明問題

其實你把B轉一轉就會變成A了

就像
12
34
與
13
24
你頭轉一轉就會知他們是一樣的東西

2011-10-17 23:58:25 補充：
剛剛那例子怪怪的
不過以3x3為例

要求determine....你會計算出6個項目
B與A的項目都是相同
所以兩者determine一樣

B is row equivalent to A iff.
for a sequence of elementary matrices E1,...,En,
B = (En)...(E1)A.
So B^{-1} = A^{-1}(E1)^{-1}...(En)^{-1}.

2011-10-14 20:30:52 補充：
Ax = 0 has only the trivial solution, means that A is full rank,
or equivalently, A is nonsingular.
Therefore, for any positive integer k, A^k is nonsingular too.
Then, A^k X = 0 has only the trivial solution.

Elementary matrix