Question

2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4

Answer 1

Date: A =1327 34 Ans- let then for eigenvalues det (A-AI) = 0 det [2] 1L 3 4J det 3-0 - :)) - O 2 4-7 3 2 2 12-37-40 + x - 6=0 X-FX +6=0 x²-2-62 +6=0 à (2-1)-6 (7-1)=0 (2-6) (2-1)=0 2-6=0 or x-1=0 2=6 for eigen Jectors x=1 Av=nu 13. 270 3 4 J L V₂ where v to eigenvector S 53V, + 27, V L3V, +4V2 3 V, + 2/₂ = V. » 2V, + 2V=0 3 V 44 V2 = V → svi + 3,00 V, 70 G Veto » V = -√₂ So,

are the eigenvectors all So eigenrectors for x=1 VERLO} for example let val then [] is one of Au=0 3 274 ] for x=1 le 34, + 2 v 1 - 5607 L3V+44 3V, + 2 V₂ = 6V, » 2V₂ = 3V 3 V+ 4W₂ = 6V₂ - 3 V = 2V₂ Se all agenvectors for x=6. V toe V 0 6V 34 16V Z V ₂ = 3 v are S VER 3ν VERsoy IR | 20} for example let val, then of one 13 is eigenved for for x=6,
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