Consider the linear transformation U: R^3 rightarrow R^3

Lennie Carroll 2020-10-20 Answered

Consider the linear transformation U:R3R3 defined by U(xyz)=(zyz+y3zxy) and the bases ϵ={(100),(010),(001)},γ={(1i1+i1),(110),(001)}, Compute the four coordinate matrices [U]ϵγ,[U]γγ,

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Expert Answer

irwchh
Answered 2020-10-21 Author has 102 answers

U(1i1+i1)=(i2+i1)=1v1+1v2+0v3
U(110)=(110)=0v1+1v2+0v3
U(011)=(022)=0v1+0v2+2v3 So, [U]γγ=[100110002]
U(100)=(001).Since(001){γ} So, [U]ϵγ does not exist U(1i1+i1)=i1ϵ1+(2+i)ϵ2+1ϵ2
U(110)=(110)=1ϵ1+1ϵ2+0ϵ3
U(011)=(021)=0ϵ1+2ϵ2+1ϵ3 So, [U]ϵγ=[i102+i12101]

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