1 0 2. LetA [6 _1]. (a) Find the eigenvalues of A and for each eigenvalue A, nd a basis of the corresponding eigenspace EA. Show your work. (b) Write…

2.Let A=[(1,6),(0,-1)] (a) Find the eigenvalues of A and for each eigenvalue λ, find a basis of the corresponding eigenspace Eλ. Show your work. (b) Write down an invertible matrix P and a diagonal matrix D such that P−1AP = D. Show that the equation P−1AP = D is satisfied for your matrices P and D. 1 02. LetA— [6 _1]. (a) Find the eigenvalues of A and for each eigenvalue A, ﬁnd a basisof the corresponding eigenspace EA. Show your work. (b) Write down an invertible matrix P and a diagonal matrix D suchthat P‘lAP = D. Show that the equation P‘lAP = D issatisﬁed for your matrices P and D.

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