以下兩題
1. x'= / 2 -1 \ x
\ 3 -2 /
2. x'= / 2 -5 \ x
\ 1 -2 /
要找:a.fundamental matrix for the given system of equation
b.fundamental matrix Φ(t) satisfying Φ(0)=I
課本後面只有給b的答案:
1. / 3 t 1 -t -1 t 1 -t \
/ ﹣e^ － ﹣e^ ﹣e^ ＋ ﹣e^ \
Φ(t)= / 2 2 2 2 \
\ 3 t 3 -t -1 t 3 -t /
\ ﹣e^ － ﹣e^ ﹣e^ ＋ ﹣e^ /
\ 2 2 2 2 /
2. Φ(t)= / cost+2sint -5sint \
\ sint cost-2sint /
真是抱歉我進度落後太多了都看不懂只好來麻煩一下板友了Orz
第一題我照課本例題的方法算出兩個特徵值正負1，特徵向量分別/1\ 跟 /1\
1 t 2 -t \1/ \3/
然後得到X (t)= / 1 \ e^ X (t)= / 1 \ e^
\ 1 / \ 3 /
再來就不曉得要怎麼做才能把它變成像答案那個樣子了~"~也不確定到這裡有沒有算錯
然後第二題就完全無法了，怎麼會突然跑出sin跟cos來...囧
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