Re: [理工] [工數]-中興95-電機所
※ 引述《uniqueco (寶)》之銘言：
: 1.
: T(1,0)=(2,7)
: T(1,1)=(4,5)
: Please find the range of T
1 0 2 7
T (1 1 ) = (4 5 )
-5 7
T = (-1 5 )
R(T) = span{[-5 -1]^t [7 5]^t }
: 2
: 2.W=sp(e^x,xe^x,x e^x)
: 2 2
: T is the matrix relative to bases B1=(e^x,xe^x,x e^x) and B2=(2xe^x,x e^x,e^x)
: be M1 and M2 ,respectively.
: -1
: find M2 and invertible matrix C such that M2=C M1C.
: 這兩題不知如何作答
: 麻煩版上高手幫忙><
: 謝謝
你題目沒給完整
他有定義T是一個微分運算子
T(2xe^x) = 2xe^x + 2e^x
T(x^2e^x) = 2xe^x +x^2e^x
T(e^x) = e^x
1 1 0
M2 = [ 0 1 0 ]
2 0 1
2. 他給的B1基底 [e^x xe^x x^2e^x]
B2 [2xe^x x^2e^x e^x] 是兩組有序的基底
B1 0 0 1
基底轉換矩陣[I] = [ 2 0 0 ]
B2 0 1 0
M2 = C^-1 M1 C
B2 B1
=[I] M1 [I]
B1 B2
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