Find a not matrix from eigenvalues and eigenvectors
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have been asked to verify whether v=[14]v=[14] is an eigenvector of A=[−3−318]A=[−31−38]? If yes, find the eigenvalue.
The way that I approached this question is to find eigenvalues, then use eigenvalues to verify whether vv is an eigenvector of the matrix. Here is how I find the eigenvalues:
∴λdet(A−λI)=det([−3−318]−[λ00λ])=det([−3−λ−318−λ])=(−3−λ)(8−λ)−(−3)=12(5±109−−−√)
det(A−λI)=det([−31−38]−[λ00λ])=det([−3−λ1−38−λ])=(−3−λ)(8−λ)−(−3)∴λ=12(5±109)
To verify:
Av=λv[−3−318][14]=[14][129]=12(5±109−−−√)[14]
The way that I approached this question is to find eigenvalues, then use eigenvalues to verify whether vv is an eigenvector of the matrix. Here is how I find the eigenvalues:
∴λdet(A−λI)=det([−3−318]−[λ00λ])=det([−3−λ−318−λ])=(−3−λ)(8−λ)−(−3)=12(5±109−−−√)
det(A−λI)=det([−31−38]−[λ00λ])=det([−3−λ1−38−λ])=(−3−λ)(8−λ)−(−3)∴λ=12(5±109)
To verify:
Av=λv[−3−318][14]=[14][129]=12(5±109−−−√)[14]
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