Question

Orthogonally diagonalize A as PDPT A = 1 5 51

Answer 1

We will onthog ogonally diagonalize A as PDPT where. A= 5 51 First we have to find el Let it be eigenvalue of a then det (A-XI) = 0 elgenvalues of A. & In EO Na 1-) => 61-X) ► 26=0 → 61-)-5)(1-1+5) = 0 zs 1-4,6 ... Eigen Eigen values of A are -4,6 Now we find eigenspace for these efgon values To find eigenspace of a=-4 we have to solve the system (A +41) 2-0 =[55] This system gives 5*,+ 58220 => Mith2=0 =22 = -2 setting hist the enlution is Der [-2] =+ L) --for eigenvalue x=-4 basis for en }} basis for this eigenspace is orthononmal that is n = elgenspace 13 - Editor ['03 that is V2 on CSScanned with CamScanner

eigen -nga na co onth this TR 1:] To find en space for 7=6 CA-6In zo $ 55-576)-[: This system is equivalent to => mE92 Setting ag at the solution is L].[1] = $(!) Basis for this eigen space is [!]} on onmal basis for eigenspace is t ŽAJ sienging the eigenspaces for the elgonrants ay and we have our orthonommal basie. { [](213 F 1, which is va orthogonal. If A= POPT then =) :D = pt A B7) te - Det // takeo pe pi (pt) = 1 + :D va CJE Ft Al- 읊 12 1/2 t T-4 0 0 Scanned:witheamScanner TO G

We have P= P is anothogonal. [ ] [2] PENSE T and A: 금초 0 Epippt C Scanned with CamScanner